LMFDB - Embedded newform 750.2.o.b.469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.2
Character	$\chi$	$=$	750.469
Dual form			750.2.o.b.379.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.24970 - 1.85425i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.29119 - 3.15355i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.24970 - 1.85425i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.29119 - 3.15355i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(1.36366 + 1.77212i) q^{10} +(-0.0420078 - 0.667694i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(-2.69231 - 2.22727i) q^{13} +(2.48468 + 3.00346i) q^{14} +(1.92026 + 1.14568i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.575193 + 4.55312i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(0.897184 - 1.90661i) q^{19} +(-1.47225 - 1.68300i) q^{20} +(3.41584 + 1.87788i) q^{21} +(0.0838498 + 0.663739i) q^{22} +(2.07004 + 5.22833i) q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.87650 + 4.63452i) q^{25} +(2.82685 + 2.05383i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-2.66836 - 2.84152i) q^{28} +(-2.61241 + 2.45322i) q^{29} +(-1.98841 - 1.02284i) q^{30} +(1.67419 + 0.211499i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(0.322300 + 0.586262i) q^{33} +(0.288165 - 4.58025i) q^{34} +(-2.98417 + 8.18942i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.19833 - 4.66718i) q^{37} +(-0.775696 + 1.95918i) q^{38} +(3.38441 + 0.868968i) q^{39} +(1.57502 + 1.58724i) q^{40} +(8.25864 + 3.26983i) q^{41} +(-3.52701 - 1.65969i) q^{42} +(4.26582 + 1.38605i) q^{43} +(-0.125361 - 0.657164i) q^{44} +(-2.22531 - 0.219033i) q^{45} +(-2.39425 - 5.08804i) q^{46} +(-12.0211 - 2.29314i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-2.53221 + 7.79333i) q^{49} +(1.58179 - 4.74320i) q^{50} +(-1.41817 - 4.36469i) q^{51} +(-2.95023 - 1.87228i) q^{52} +(-5.23230 + 9.51751i) q^{53} +(0.187381 - 0.982287i) q^{54} +(-1.18558 + 0.912311i) q^{55} +(2.84152 + 2.66836i) q^{56} +2.10716i q^{57} +(2.45322 - 2.61241i) q^{58} +(-0.322922 - 0.508843i) q^{59} +(2.04871 + 0.895973i) q^{60} +(-10.3381 + 4.09315i) q^{61} +(-1.68417 - 0.105959i) q^{62} +(-3.89031 - 0.244757i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-0.765341 + 7.77565i) q^{65} +(-0.358476 - 0.564868i) q^{66} +(4.17608 - 4.44707i) q^{67} +4.58931i q^{68} +(-4.09915 - 3.84936i) q^{69} +(2.46406 - 8.36064i) q^{70} +(1.53206 - 8.03134i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-6.29061 - 3.99215i) q^{73} +(1.48902 + 4.58273i) q^{74} +(-0.275379 - 4.99241i) q^{75} +(0.651147 - 2.00402i) q^{76} +(-2.00936 + 1.66229i) q^{77} +(-3.43229 - 0.654744i) q^{78} +(5.27364 + 11.2070i) q^{79} +(-1.67157 - 1.48521i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-8.44766 - 2.74481i) q^{82} +(2.63913 + 1.24188i) q^{83} +(3.62427 + 1.43495i) q^{84} +(9.16145 - 4.62349i) q^{85} +(-4.34443 - 1.11546i) q^{86} +(1.31925 - 3.33205i) q^{87} +(0.166377 + 0.647996i) q^{88} +(-8.74891 + 13.7861i) q^{89} +(2.23468 + 0.0788722i) q^{90} +(-0.855227 + 13.5934i) q^{91} +(2.70900 + 4.92766i) q^{92} +(-1.60491 + 0.521465i) q^{93} +(12.1413 + 1.53381i) q^{94} +(-4.65655 + 0.719091i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-0.00201516 - 0.00214593i) q^{97} +(2.03786 - 7.93695i) q^{98} +(-0.541244 - 0.393237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	−1.24970	−	1.85425i	−0.558883	−	0.829246i
$5$	−1.24970	−	1.85425i	−0.558883	−	0.829246i
$6$	0.876307	−	0.481754i	0.357751	−	0.196675i
$7$	−2.29119	−	3.15355i	−0.865987	−	1.19193i	−0.980109	−	0.198462i	$-0.936405\pi$
$7$	−2.29119	−	3.15355i	−0.865987	−	1.19193i	0.114122	−	0.993467i	$-0.463595\pi$
$8$	−0.982287	+	0.187381i	−0.347291	+	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	1.36366	+	1.77212i	0.431229	+	0.560394i
$11$	−0.0420078	−	0.667694i	−0.0126658	−	0.201317i	−0.999271	−	0.0381884i	$-0.987841\pi$
$11$	−0.0420078	−	0.667694i	−0.0126658	−	0.201317i	0.986605	−	0.163129i	$-0.0521587\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	−2.69231	−	2.22727i	−0.746713	−	0.617735i	0.184237	−	0.982882i	$-0.441019\pi$
$13$	−2.69231	−	2.22727i	−0.746713	−	0.617735i	−0.930950	+	0.365147i	$0.881019\pi$
$14$	2.48468	+	3.00346i	0.664058	+	0.802708i
$15$	1.92026	+	1.14568i	0.495810	+	0.295813i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	−0.575193	+	4.55312i	−0.139505	+	1.10429i	0.754520	+	0.656277i	$0.227870\pi$
$17$	−0.575193	+	4.55312i	−0.139505	+	1.10429i	−0.894025	+	0.448017i	$0.852130\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	0.897184	−	1.90661i	0.205828	−	0.437407i	−0.775084	−	0.631858i	$-0.782293\pi$
$19$	0.897184	−	1.90661i	0.205828	−	0.437407i	0.980912	+	0.194451i	$0.0622926\pi$
$20$	−1.47225	−	1.68300i	−0.329204	−	0.376330i
$21$	3.41584	+	1.87788i	0.745398	+	0.409786i
$22$	0.0838498	+	0.663739i	0.0178768	+	0.141510i
$23$	2.07004	+	5.22833i	0.431634	+	1.09018i	0.969050	+	0.246865i	$0.0794006\pi$
$23$	2.07004	+	5.22833i	0.431634	+	1.09018i	−0.537416	+	0.843317i	$0.680599\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−1.87650	+	4.63452i	−0.375299	+	0.926904i
$26$	2.82685	+	2.05383i	0.554391	+	0.402789i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	−2.66836	−	2.84152i	−0.504273	−	0.536997i
$29$	−2.61241	+	2.45322i	−0.485113	+	0.455551i	−0.888097	−	0.459656i	$-0.847973\pi$
$29$	−2.61241	+	2.45322i	−0.485113	+	0.455551i	0.402985	+	0.915207i	$0.367973\pi$
$30$	−1.98841	−	1.02284i	−0.363033	−	0.186745i
$31$	1.67419	+	0.211499i	0.300694	+	0.0379864i	0.274233	−	0.961663i	$-0.411576\pi$
$31$	1.67419	+	0.211499i	0.300694	+	0.0379864i	0.0264610	+	0.999650i	$0.491576\pi$
$32$	−0.951057	+	0.309017i	−0.168125	+	0.0546270i
$33$	0.322300	+	0.586262i	0.0561053	+	0.102055i
$34$	0.288165	−	4.58025i	0.0494199	−	0.785507i
$35$	−2.98417	+	8.18942i	−0.504417	+	1.38427i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	−1.19833	−	4.66718i	−0.197004	−	0.767280i	−0.987869	−	0.155289i	$-0.950369\pi$
$37$	−1.19833	−	4.66718i	−0.197004	−	0.767280i	0.790865	−	0.611990i	$-0.209631\pi$
$38$	−0.775696	+	1.95918i	−0.125835	+	0.317822i
$39$	3.38441	+	0.868968i	0.541939	+	0.139146i
$40$	1.57502	+	1.58724i	0.249032	+	0.250964i
$41$	8.25864	+	3.26983i	1.28978	+	0.510661i	0.910074	−	0.414445i	$-0.136024\pi$
$41$	8.25864	+	3.26983i	1.28978	+	0.510661i	0.379708	+	0.925106i	$0.376024\pi$
$42$	−3.52701	−	1.65969i	−0.544230	−	0.256095i
$43$	4.26582	+	1.38605i	0.650532	+	0.211371i	0.615648	−	0.788021i	$-0.288894\pi$
$43$	4.26582	+	1.38605i	0.650532	+	0.211371i	0.0348830	+	0.999391i	$0.488894\pi$
$44$	−0.125361	−	0.657164i	−0.0188989	−	0.0990713i
$45$	−2.22531	−	0.219033i	−0.331730	−	0.0326515i
$46$	−2.39425	−	5.08804i	−0.353013	−	0.750190i
$47$	−12.0211	−	2.29314i	−1.75345	−	0.334489i	−0.792223	−	0.610231i	$-0.791076\pi$
$47$	−12.0211	−	2.29314i	−1.75345	−	0.334489i	−0.961232	+	0.275742i	$0.911076\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	−2.53221	+	7.79333i	−0.361744	+	1.11333i
$50$	1.58179	−	4.74320i	0.223699	−	0.670790i
$51$	−1.41817	−	4.36469i	−0.198584	−	0.611179i
$52$	−2.95023	−	1.87228i	−0.409124	−	0.259638i
$53$	−5.23230	+	9.51751i	−0.718711	+	1.30733i	0.224284	+	0.974524i	$0.427996\pi$
$53$	−5.23230	+	9.51751i	−0.718711	+	1.30733i	−0.942995	+	0.332807i	$0.892004\pi$
$54$	0.187381	−	0.982287i	0.0254994	−	0.133672i
$55$	−1.18558	+	0.912311i	−0.159863	+	0.123016i
$56$	2.84152	+	2.66836i	0.379714	+	0.356575i
$57$			2.10716i			0.279100i
$58$	2.45322	−	2.61241i	0.322123	−	0.343026i
$59$	−0.322922	−	0.508843i	−0.0420408	−	0.0662457i	0.822658	−	0.568537i	$-0.192490\pi$
$59$	−0.322922	−	0.508843i	−0.0420408	−	0.0662457i	−0.864698	+	0.502291i	$0.832490\pi$
$60$	2.04871	+	0.895973i	0.264488	+	0.115670i
$61$	−10.3381	+	4.09315i	−1.32366	+	0.524074i	−0.920388	−	0.391006i	$-0.872127\pi$
$61$	−10.3381	+	4.09315i	−1.32366	+	0.524074i	−0.403272	+	0.915080i	$0.632127\pi$
$62$	−1.68417	−	0.105959i	−0.213889	−	0.0134568i
$63$	−3.89031	−	0.244757i	−0.490133	−	0.0308365i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−0.765341	+	7.77565i	−0.0949289	+	0.964451i
$66$	−0.358476	−	0.564868i	−0.0441253	−	0.0695304i
$67$	4.17608	−	4.44707i	0.510189	−	0.543296i	−0.421369	−	0.906889i	$-0.638450\pi$
$67$	4.17608	−	4.44707i	0.510189	−	0.543296i	0.931558	+	0.363593i	$0.118450\pi$
$68$			4.58931i			0.556535i
$69$	−4.09915	−	3.84936i	−0.493479	−	0.463408i
$70$	2.46406	−	8.36064i	0.294512	−	0.999288i
$71$	1.53206	−	8.03134i	0.181822	−	0.953145i	−0.768023	−	0.640423i	$-0.778759\pi$
$71$	1.53206	−	8.03134i	0.181822	−	0.953145i	0.949845	−	0.312722i	$-0.101241\pi$
$72$	−0.481754	+	0.876307i	−0.0567752	+	0.103274i
$73$	−6.29061	−	3.99215i	−0.736261	−	0.467245i	0.114084	−	0.993471i	$-0.463607\pi$
$73$	−6.29061	−	3.99215i	−0.736261	−	0.467245i	−0.850345	+	0.526226i	$0.823607\pi$
$74$	1.48902	+	4.58273i	0.173095	+	0.532731i
$75$	−0.275379	−	4.99241i	−0.0317980	−	0.576474i
$76$	0.651147	−	2.00402i	0.0746917	−	0.229877i
$77$	−2.00936	+	1.66229i	−0.228988	+	0.189435i
$78$	−3.43229	−	0.654744i	−0.388630	−	0.0741352i
$79$	5.27364	+	11.2070i	0.593330	+	1.26089i	0.945703	+	0.325031i	$0.105375\pi$
$79$	5.27364	+	11.2070i	0.593330	+	1.26089i	−0.352373	+	0.935860i	$0.614625\pi$
$80$	−1.67157	−	1.48521i	−0.186888	−	0.166051i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	−8.44766	−	2.74481i	−0.932888	−	0.303114i
$83$	2.63913	+	1.24188i	0.289682	+	0.136314i	0.565130	−	0.825002i	$-0.308826\pi$
$83$	2.63913	+	1.24188i	0.289682	+	0.136314i	−0.275448	+	0.961316i	$0.588826\pi$
$84$	3.62427	+	1.43495i	0.395440	+	0.156566i
$85$	9.16145	−	4.62349i	0.993698	−	0.501487i
$86$	−4.34443	−	1.11546i	−0.468472	−	0.120283i
$87$	1.31925	−	3.33205i	0.141439	−	0.357233i
$88$	0.166377	+	0.647996i	0.0177359	+	0.0690766i
$89$	−8.74891	+	13.7861i	−0.927383	+	1.46132i	−0.0405790	+	0.999176i	$0.512920\pi$
$89$	−8.74891	+	13.7861i	−0.927383	+	1.46132i	−0.886804	+	0.462146i	$0.847080\pi$
$90$	2.23468	+	0.0788722i	0.235556	+	0.00831386i
$91$	−0.855227	+	13.5934i	−0.0896521	+	1.42498i
$92$	2.70900	+	4.92766i	0.282433	+	0.513744i
$93$	−1.60491	+	0.521465i	−0.166421	+	0.0540734i
$94$	12.1413	+	1.53381i	1.25228	+	0.158200i
$95$	−4.65655	+	0.719091i	−0.477752	+	0.0737772i
$96$	0.728969	−	0.684547i	0.0744000	−	0.0698663i
$97$	−0.00201516	−	0.00214593i	−0.000204608	−	0.000217886i	0.728866	−	0.684656i	$-0.240048\pi$
$97$	−0.00201516	−	0.00214593i	−0.000204608	−	0.000217886i	−0.729071	+	0.684438i	$0.760048\pi$
$98$	2.03786	−	7.93695i	0.205855	−	0.801753i
$99$	−0.541244	−	0.393237i	−0.0543971	−	0.0395218i
$100$	−1.28084	+	4.83316i	−0.128084	+	0.483316i
$101$	−6.64399	+	4.82714i	−0.661102	+	0.480319i	−0.867035	−	0.498247i	$-0.833977\pi$
$101$	−6.64399	+	4.82714i	−0.661102	+	0.480319i	0.205933	+	0.978566i	$0.433977\pi$
$102$	1.68944	+	4.26703i	0.167279	+	0.422499i
$103$	0.763355	+	6.04258i	0.0752156	+	0.595393i	0.984005	+	0.178139i	$0.0570076\pi$
$103$	0.763355	+	6.04258i	0.0752156	+	0.595393i	−0.908790	+	0.417254i	$0.862992\pi$
$104$	3.06197	+	1.68333i	0.300251	+	0.165065i
$105$	−0.786729	−	8.68061i	−0.0767769	−	0.847141i
$106$	4.62436	−	9.82727i	0.449158	−	0.954509i
$107$	7.07825	−	9.74238i	0.684281	−	0.941832i	−0.315695	−	0.948861i	$-0.602238\pi$
$107$	7.07825	−	9.74238i	0.684281	−	0.941832i	0.999975	+	0.00702933i	$0.00223752\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	−8.08733	+	2.07647i	−0.774626	+	0.198890i	−0.615255	−	0.788329i	$-0.710947\pi$
$109$	−8.08733	+	2.07647i	−0.774626	+	0.198890i	−0.159371	+	0.987219i	$0.550947\pi$
$110$	1.12595	−	0.984954i	0.107355	−	0.0939117i
$111$	3.07147	+	3.71277i	0.291531	+	0.352400i
$112$	−3.00346	−	2.48468i	−0.283800	−	0.234780i
$113$	−10.4671	+	6.64259i	−0.984658	+	0.624883i	−0.927634	−	0.373490i	$-0.878161\pi$
$113$	−10.4671	+	6.64259i	−0.984658	+	0.624883i	−0.0570234	+	0.998373i	$0.518161\pi$
$114$	−0.132309	−	2.10300i	−0.0123919	−	0.196964i
$115$	7.10771	−	10.3722i	0.662797	−	0.967216i
$116$	−2.28434	+	2.76129i	−0.212096	+	0.256380i
$117$	−3.43229	+	0.654744i	−0.317315	+	0.0605311i
$118$	0.354235	+	0.487563i	0.0326100	+	0.0448838i
$119$	15.6763	−	8.61815i	1.43705	−	0.790024i
$120$	−2.10093	−	0.765565i	−0.191788	−	0.0698862i
$121$	10.4692	−	1.32257i	0.951746	−	0.120234i
$122$	10.0607	−	4.73421i	0.910854	−	0.428615i
$123$	−8.86486	+	0.557730i	−0.799318	+	0.0502888i
$124$	1.68750			0.151542
$125$	10.9386	−	2.31227i	0.978380	−	0.206816i
$126$	3.89800			0.347261
$127$	−4.75078	+	0.298894i	−0.421564	+	0.0265226i	−0.272156	−	0.962253i	$-0.587737\pi$
$127$	−4.75078	+	0.298894i	−0.421564	+	0.0265226i	−0.149408	+	0.988776i	$0.547737\pi$
$128$	−0.904827	+	0.425779i	−0.0799762	+	0.0376339i
$129$	−4.44998	+	0.562163i	−0.391799	+	0.0494957i
$130$	0.275594	−	7.80836i	0.0241712	−	0.684839i
$131$	−0.185585	+	0.102026i	−0.0162146	+	0.00891407i	−0.489840	−	0.871812i	$-0.662945\pi$
$131$	−0.185585	+	0.102026i	−0.0162146	+	0.00891407i	0.473626	+	0.880726i	$0.342945\pi$
$132$	0.393237	+	0.541244i	0.0342269	+	0.0471093i
$133$	−8.06820	+	1.53909i	−0.699602	+	0.133456i
$134$	−3.88860	+	4.70051i	−0.335924	+	0.406063i
$135$	2.10678	−	0.749306i	0.181323	−	0.0644900i
$136$	−0.288165	−	4.58025i	−0.0247099	−	0.392753i
$137$	9.83321	−	6.24035i	0.840108	−	0.533149i	−0.0447562	−	0.998998i	$-0.514251\pi$
$137$	9.83321	−	6.24035i	0.840108	−	0.533149i	0.884864	+	0.465849i	$0.154251\pi$
$138$	4.33276	+	3.58437i	0.368829	+	0.305122i
$139$	5.74415	+	6.94349i	0.487213	+	0.588939i	0.955631	−	0.294568i	$-0.0951757\pi$
$139$	5.74415	+	6.94349i	0.487213	+	0.588939i	−0.468418	+	0.883507i	$0.655176\pi$
$140$	−1.93423	+	8.49886i	−0.163473	+	0.718285i
$141$	11.8534	−	3.04343i	0.998234	−	0.256303i
$142$	−1.02475	+	8.11169i	−0.0859947	+	0.680718i
$143$	−1.37404	+	1.89121i	−0.114903	+	0.158151i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	7.81361	+	1.77828i	0.648885	+	0.147678i
$146$	6.52887	+	3.58928i	0.540333	+	0.297051i
$147$	−1.02703	−	8.12978i	−0.0847080	−	0.670533i
$148$	−1.77383	−	4.48019i	−0.145808	−	0.368269i
$149$	6.87214	−	4.99291i	0.562988	−	0.409035i	−0.269563	−	0.962983i	$-0.586879\pi$
$149$	6.87214	−	4.99291i	0.562988	−	0.409035i	0.832551	+	0.553948i	$0.186879\pi$
$150$	0.588311	+	4.96527i	0.0480354	+	0.405412i
$151$	−14.4613	−	10.5068i	−1.17685	−	0.855029i	−0.185034	−	0.982732i	$-0.559240\pi$
$151$	−14.4613	−	10.5068i	−1.17685	−	0.855029i	−0.991812	+	0.127703i	$0.959240\pi$
$152$	−0.524028	+	2.04096i	−0.0425043	+	0.165543i
$153$	3.14160	+	3.34546i	0.253983	+	0.270464i
$154$	1.90102	−	1.78517i	0.153188	−	0.143853i
$155$	−1.70006	−	3.36868i	−0.136552	−	0.270579i
$156$	3.46663	+	0.437937i	0.277552	+	0.0350630i
$157$	10.8553	−	3.52711i	0.866349	−	0.281494i	0.158071	−	0.987428i	$-0.449473\pi$
$157$	10.8553	−	3.52711i	0.866349	−	0.281494i	0.708278	+	0.705934i	$0.249473\pi$
$158$	−5.96693	−	10.8538i	−0.474703	−	0.863482i
$159$	0.681964	−	10.8395i	0.0540832	−	0.859629i
$160$	1.76153	+	1.37732i	0.139261	+	0.108887i
$161$	11.7449	−	18.5071i	0.925631	−	1.45856i
$162$	0.248690	+	0.968583i	0.0195389	+	0.0760991i
$163$	2.52100	−	6.36733i	0.197460	−	0.498728i	−0.796983	−	0.604002i	$-0.793572\pi$
$163$	2.52100	−	6.36733i	0.197460	−	0.498728i	0.994443	+	0.105274i	$0.0335720\pi$
$164$	8.60334	+	2.20896i	0.671808	+	0.172491i
$165$	0.684298	−	1.33028i	0.0532725	−	0.103562i
$166$	−2.71190	−	1.07372i	−0.210484	−	0.0833367i
$167$	−10.3844	−	4.88652i	−0.803568	−	0.378130i	−0.0202836	−	0.999794i	$-0.506457\pi$
$167$	−10.3844	−	4.88652i	−0.803568	−	0.378130i	−0.783284	+	0.621664i	$0.786457\pi$
$168$	−3.70722	−	1.20455i	−0.286018	−	0.0929329i
$169$	−0.148162	−	0.776692i	−0.0113971	−	0.0597455i
$170$	−8.85306	+	5.18961i	−0.678998	+	0.398025i
$171$	−0.897184	−	1.90661i	−0.0686093	−	0.145802i
$172$	4.40590	+	0.840471i	0.335947	+	0.0640853i
$173$	0.342436	−	0.283287i	0.0260349	−	0.0215379i	−0.624316	−	0.781172i	$-0.714622\pi$
$173$	0.342436	−	0.283287i	0.0260349	−	0.0215379i	0.650350	+	0.759634i	$0.274622\pi$
$174$	−1.10743	+	3.40831i	−0.0839538	+	0.258383i
$175$	18.9146	−	4.70093i	1.42981	−	0.355357i
$176$	−0.206737	−	0.636271i	−0.0155834	−	0.0479607i
$177$	0.508843	+	0.322922i	0.0382470	+	0.0242723i
$178$	7.86602	−	14.3082i	0.589583	−	1.07245i
$179$	−0.901816	+	4.72749i	−0.0674049	+	0.353349i	−0.999971	−	0.00765105i	$-0.997565\pi$
$179$	−0.901816	+	4.72749i	−0.0674049	+	0.353349i	0.932566	+	0.361000i	$0.117565\pi$
$180$	−2.23522	+	0.0615999i	−0.166603	+	0.00459139i
$181$	−16.6853	−	15.6685i	−1.24020	−	1.16463i	−0.979983	−	0.199081i	$-0.936204\pi$
$181$	−16.6853	−	15.6685i	−1.24020	−	1.16463i	−0.260222	−	0.965549i	$-0.583796\pi$
$182$		−	13.6203i		−	1.00960i
$183$	7.61143	−	8.10535i	0.562653	−	0.599165i
$184$	−3.01307	−	4.74784i	−0.222126	−	0.350015i
$185$	−7.15657	+	8.05458i	−0.526162	+	0.592185i
$186$	1.56900	−	0.621209i	0.115044	−	0.0455493i
$187$	3.06425	+	0.192787i	0.224081	+	0.0140980i
$188$	−12.2137	−	0.768421i	−0.890775	−	0.0560428i
$189$	3.62427	−	1.43495i	0.263627	−	0.104377i
$190$	4.60221	−	1.01006i	0.333879	−	0.0732774i
$191$	−11.1343	−	17.5449i	−0.805650	−	1.26950i	−0.959585	−	0.281420i	$-0.909194\pi$
$191$	−11.1343	−	17.5449i	−0.805650	−	1.26950i	0.153934	−	0.988081i	$-0.450806\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$			24.1087i			1.73538i	0.497104	+	0.867691i	$0.334397\pi$
$193$			24.1087i			1.73538i	−0.497104	+	0.867691i	$0.665603\pi$
$194$	0.00214593	+	0.00201516i	0.000154069	+	0.000144680i
$195$	−2.61821	−	7.36149i	−0.187494	−	0.527167i
$196$	−1.53548	+	8.04925i	−0.109677	+	0.574946i
$197$	−1.76867	+	3.21720i	−0.126013	+	0.229216i	−0.931786	−	0.363008i	$-0.881750\pi$
$197$	−1.76867	+	3.21720i	−0.126013	+	0.229216i	0.805773	+	0.592224i	$0.201750\pi$
$198$	0.564868	+	0.358476i	0.0401434	+	0.0254758i
$199$	−2.94994	−	9.07899i	−0.209116	−	0.643593i	−0.999519	−	0.0310058i	$-0.990129\pi$
$199$	−2.94994	−	9.07899i	−0.209116	−	0.643593i	0.790403	−	0.612587i	$-0.209871\pi$
$200$	0.974835	−	4.90405i	0.0689312	−	0.346769i
$201$	−1.88516	+	5.80192i	−0.132969	+	0.409236i
$202$	6.32779	−	5.23480i	0.445221	−	0.368319i
$203$	13.7219	+	2.61758i	0.963085	+	0.183718i
$204$	−1.95403	−	4.15253i	−0.136810	−	0.290735i
$205$	−4.25775	−	19.3999i	−0.297374	−	1.35495i
$206$	−1.14127	−	5.98273i	−0.0795158	−	0.416836i
$207$	5.34800	+	1.73767i	0.371711	+	0.120776i
$208$	−3.16163	−	1.48775i	−0.219220	−	0.103157i
$209$	−1.31072	−	0.518952i	−0.0906646	−	0.0358967i
$210$	1.33024	+	8.61408i	0.0917950	+	0.594428i
$211$	23.3018	+	5.98289i	1.60416	+	0.411879i	0.941493	−	0.337032i	$-0.109423\pi$
$211$	23.3018	+	5.98289i	1.60416	+	0.411879i	0.662671	+	0.748911i	$0.269423\pi$
$212$	−3.99818	+	10.0982i	−0.274596	+	0.693550i
$213$	2.03333	+	7.91929i	0.139321	+	0.542621i
$214$	−6.45256	+	10.1676i	−0.441088	+	0.695043i
$215$	−2.76092	−	9.64205i	−0.188293	−	0.657582i
$216$	0.0627905	−	0.998027i	0.00427235	−	0.0679071i
$217$	−3.16891	−	5.76422i	−0.215120	−	0.391301i
$218$	7.94099	−	2.58018i	0.537832	−	0.174752i
$219$	7.39169	+	0.933788i	0.499484	+	0.0630995i
$220$	−1.06188	+	1.05371i	−0.0715922	+	0.0710411i
$221$	11.6896	−	10.9773i	0.786331	−	0.738414i
$222$	−3.29853	−	3.51258i	−0.221383	−	0.235749i
$223$	−0.158945	+	0.619051i	−0.0106438	+	0.0414547i	−0.973683	−	0.227906i	$-0.926812\pi$
$223$	−0.158945	+	0.619051i	−0.0106438	+	0.0414547i	0.963039	+	0.269360i	$0.0868122\pi$
$224$	3.15355	+	2.29119i	0.210705	+	0.153086i
$225$	2.37484	+	4.40002i	0.158322	+	0.293335i
$226$	10.0293	−	7.28672i	0.667140	−	0.484705i
$227$	−4.23033	−	10.6846i	−0.280777	−	0.709161i	−0.999898	−	0.0142764i	$-0.995456\pi$
$227$	−4.23033	−	10.6846i	−0.280777	−	0.709161i	0.719121	−	0.694884i	$-0.244544\pi$
$228$	0.264097	+	2.09054i	0.0174902	+	0.138449i
$229$	−6.06166	−	3.33243i	−0.400566	−	0.220213i	0.268719	−	0.963218i	$-0.413400\pi$
$229$	−6.06166	−	3.33243i	−0.400566	−	0.220213i	−0.669285	+	0.743006i	$0.733400\pi$
$230$	−6.44240	+	10.7981i	−0.424800	+	0.712003i
$231$	1.11035	−	2.35962i	0.0730560	−	0.155252i
$232$	2.10645	−	2.89928i	0.138295	−	0.190347i
$233$	−3.15166	+	24.9480i	−0.206472	+	1.63440i	0.459328	+	0.888267i	$0.348090\pi$
$233$	−3.15166	+	24.9480i	−0.206472	+	1.63440i	−0.665801	+	0.746130i	$0.731910\pi$
$234$	3.38441	−	0.868968i	0.221245	−	0.0568062i
$235$	10.7707	+	25.1558i	0.702602	+	1.64099i
$236$	−0.384150	−	0.464358i	−0.0250061	−	0.0302271i
$237$	−9.54346	−	7.89503i	−0.619914	−	0.512838i
$238$	−15.1043	+	9.58547i	−0.979065	+	0.621333i
$239$	0.841160	+	13.3699i	0.0544101	+	0.864824i	0.926692	+	0.375821i	$0.122639\pi$
$239$	0.841160	+	13.3699i	0.0544101	+	0.864824i	−0.872282	+	0.489003i	$0.837361\pi$
$240$	2.14486	+	0.632136i	0.138450	+	0.0408042i
$241$	−15.4350	+	18.6577i	−0.994255	+	1.20185i	−0.0148605	+	0.999890i	$0.504730\pi$
$241$	−15.4350	+	18.6577i	−0.994255	+	1.20185i	−0.979394	+	0.201958i	$0.935270\pi$
$242$	−10.3655	+	1.97733i	−0.666320	+	0.127107i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	−9.74359	+	5.35659i	−0.623770	+	0.342920i
$245$	17.6153	−	5.04398i	1.12540	−	0.322248i
$246$	8.81235	−	1.11326i	0.561855	−	0.0709788i
$247$	−6.66205	+	3.13492i	−0.423896	+	0.199470i
$248$	−1.68417	+	0.105959i	−0.106945	+	0.00672839i
$249$	−2.91672			−0.184840
$250$	−10.7718	+	2.99455i	−0.681271	+	0.189392i
$251$	2.22618			0.140515			0.0702576	−	0.997529i	$-0.477618\pi$
$251$	2.22618			0.140515			0.0702576	+	0.997529i	$0.477618\pi$
$252$	−3.89031	+	0.244757i	−0.245066	+	0.0154183i
$253$	3.40397	−	1.60179i	0.214006	−	0.100703i
$254$	4.72264	−	0.596608i	0.296325	−	0.0374345i
$255$	−6.32094	+	8.08421i	−0.395833	+	0.506253i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−11.2886	−	15.5374i	−0.704160	−	0.969194i	−0.999903	−	0.0139260i	$-0.995567\pi$
$257$	−11.2886	−	15.5374i	−0.704160	−	0.969194i	0.295743	−	0.955268i	$-0.404433\pi$
$258$	4.40590	−	0.840471i	0.274299	−	0.0523254i
$259$	−11.9726	+	14.4724i	−0.743940	+	0.899269i
$260$	0.215241	+	7.81026i	0.0133487	+	0.484372i
$261$	0.225023	+	3.57664i	0.0139286	+	0.221388i
$262$	0.178812	−	0.113478i	0.0110471	−	0.00701068i
$263$	19.9605	+	16.5128i	1.23082	+	1.01822i	0.998966	+	0.0454702i	$0.0144786\pi$
$263$	19.9605	+	16.5128i	1.23082	+	1.01822i	0.231852	+	0.972751i	$0.425521\pi$
$264$	−0.426446	−	0.515485i	−0.0262459	−	0.0317259i
$265$	24.1867	−	2.19205i	1.48577	−	0.134657i
$266$	7.95564	−	2.04266i	0.487792	−	0.125244i
$267$	2.04643	−	16.1991i	0.125239	−	0.991370i
$268$	3.58578	−	4.93541i	0.219037	−	0.301478i
$269$	2.62466	−	5.57769i	0.160028	−	0.340078i	−0.808692	−	0.588232i	$-0.799824\pi$
$269$	2.62466	−	5.57769i	0.160028	−	0.340078i	0.968720	+	0.248155i	$0.0798241\pi$
$270$	−2.05558	+	0.880113i	−0.125098	+	0.0535620i
$271$	−12.9711	−	7.13092i	−0.787938	−	0.433173i	0.0363527	−	0.999339i	$-0.488426\pi$
$271$	−12.9711	−	7.13092i	−0.787938	−	0.433173i	−0.824291	+	0.566166i	$0.808426\pi$
$272$	0.575193	+	4.55312i	0.0348762	+	0.276073i
$273$	−5.01397	−	12.6638i	−0.303459	−	0.766451i
$274$	−9.42197	+	6.84546i	−0.569202	+	0.413550i
$275$	3.17327	+	1.05824i	0.191355	+	0.0638142i
$276$	−4.54928	−	3.30524i	−0.273834	−	0.198952i
$277$	−4.60966	+	17.9534i	−0.276967	+	1.07872i	0.666032	+	0.745923i	$0.267991\pi$
$277$	−4.60966	+	17.9534i	−0.276967	+	1.07872i	−0.943000	+	0.332794i	$0.892009\pi$
$278$	−6.16881	−	6.56911i	−0.369980	−	0.393989i
$279$	1.23013	−	1.15517i	0.0736461	−	0.0691583i
$280$	1.39677	−	8.60355i	0.0834728	−	0.514160i
$281$	−28.0177	−	3.53946i	−1.67140	−	0.211147i	−0.768151	−	0.640269i	$-0.778823\pi$
$281$	−28.0177	−	3.53946i	−1.67140	−	0.211147i	−0.903246	+	0.429122i	$0.858823\pi$
$282$	−11.6389	+	3.78170i	−0.693085	+	0.225197i
$283$	−0.497354	−	0.904684i	−0.0295646	−	0.0537779i	0.861112	−	0.508416i	$-0.169769\pi$
$283$	−0.497354	−	0.904684i	−0.0295646	−	0.0537779i	−0.890676	+	0.454638i	$0.849769\pi$
$284$	0.513386	−	8.16003i	0.0304638	−	0.484209i
$285$	3.90720	−	2.63332i	0.231442	−	0.155984i
$286$	1.25258	−	1.97375i	0.0740666	−	0.116710i
$287$	−8.61053	−	33.5358i	−0.508263	−	1.97955i
$288$	−0.368125	+	0.929776i	−0.0216919	+	0.0547876i
$289$	−3.93413	−	1.01011i	−0.231420	−	0.0594185i
$290$	−7.90985	−	1.28415i	−0.464483	−	0.0754078i
$291$	0.00273706	+	0.00108368i	0.000160449	+	6.35264e-5i
$292$	−6.74136	−	3.17224i	−0.394508	−	0.185641i
$293$	20.9621	+	6.81099i	1.22462	+	0.397902i	0.848762	−	0.528776i	$-0.177349\pi$
$293$	20.9621	+	6.81099i	1.22462	+	0.397902i	0.375856	+	0.926678i	$0.377349\pi$
$294$	1.53548	+	8.04925i	0.0895508	+	0.469442i
$295$	−0.539967	+	1.23468i	−0.0314381	+	0.0718858i
$296$	2.05164	+	4.35997i	0.119249	+	0.253418i
$297$	0.657164	+	0.125361i	0.0381325	+	0.00727417i
$298$	−6.54508	+	5.41456i	−0.379146	+	0.313657i
$299$	6.07173	−	18.6869i	0.351137	−	1.08069i
$300$	−0.898922	−	4.91853i	−0.0518993	−	0.283971i
$301$	−5.40282	−	16.6282i	−0.311413	−	0.958431i
$302$	15.0925	+	9.57801i	0.868477	+	0.551152i
$303$	3.95637	−	7.19661i	0.227287	−	0.413434i
$304$	0.394842	−	2.06983i	0.0226457	−	0.118713i
$305$	20.5093	+	14.0543i	1.17436	+	0.804744i
$306$	−3.34546	−	3.14160i	−0.191247	−	0.179593i
$307$			11.7889i			0.672830i	0.941714	+	0.336415i	$0.109215\pi$
$307$			11.7889i			0.672830i	−0.941714	+	0.336415i	$0.890785\pi$
$308$	−1.78517	+	1.90102i	−0.101720	+	0.108321i
$309$	−3.26351	−	5.14247i	−0.185655	−	0.292545i
$310$	1.90823	+	3.25529i	0.108380	+	0.184888i
$311$	−10.3017	+	4.07871i	−0.584153	+	0.231283i	−0.641566	−	0.767068i	$-0.721715\pi$
$311$	−10.3017	+	4.07871i	−0.584153	+	0.231283i	0.0574128	+	0.998351i	$0.481715\pi$
$312$	−3.48729	−	0.219401i	−0.197429	−	0.0124212i
$313$	−16.6870	−	1.04986i	−0.943208	−	0.0593416i	−0.416266	−	0.909243i	$-0.636661\pi$
$313$	−16.6870	−	1.04986i	−0.943208	−	0.0593416i	−0.526942	+	0.849901i	$0.676661\pi$
$314$	−10.6124	+	4.20176i	−0.598894	+	0.237119i
$315$	4.40788	+	7.51948i	0.248356	+	0.423675i
$316$	6.63667	+	10.4577i	0.373342	+	0.588292i
$317$	−1.71780	+	1.82927i	−0.0964810	+	0.102742i	−0.775397	−	0.631474i	$-0.782450\pi$
$317$	−1.71780	+	1.82927i	−0.0964810	+	0.102742i	0.678916	+	0.734216i	$0.262450\pi$
$318$			10.8609i			0.609051i
$319$	1.74774	+	1.64124i	0.0978547	+	0.0918917i
$320$	−1.84454	−	1.26399i	−0.103113	−	0.0706594i
$321$	−2.25649	+	11.8289i	−0.125945	+	0.660227i
$322$	−10.5597	+	19.2080i	−0.588469	+	1.07042i
$323$	8.16498	+	5.18165i	0.454312	+	0.288315i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	15.3745	−	8.29810i	0.852822	−	0.460296i
$326$	−2.11622	+	6.51306i	−0.117207	+	0.360725i
$327$	6.43352	−	5.32227i	0.355774	−	0.294322i
$328$	−8.72506	−	1.66439i	−0.481761	−	0.0919008i
$329$	20.3110	+	43.1631i	1.11978	+	2.37966i
$330$	−0.599419	+	1.37062i	−0.0329969	+	0.0754502i
$331$	−2.85108	−	14.9459i	−0.156710	−	0.821501i	−0.970640	−	0.240538i	$-0.922676\pi$
$331$	−2.85108	−	14.9459i	−0.156710	−	0.821501i	0.813930	−	0.580963i	$-0.197324\pi$
$332$	2.77397	+	0.901317i	0.152241	+	0.0494662i
$333$	−4.35997	−	2.05164i	−0.238925	−	0.112429i
$334$	10.6707	+	4.22484i	0.583876	+	0.231173i
$335$	−13.4648	−	2.18599i	−0.735663	−	0.119433i
$336$	3.77554	+	0.969393i	0.205972	+	0.0528847i
$337$	−2.00097	+	5.05387i	−0.109000	+	0.275302i	−0.974030	−	0.226417i	$-0.927299\pi$
$337$	−2.00097	+	5.05387i	−0.109000	+	0.275302i	0.865031	+	0.501719i	$0.167299\pi$
$338$	0.196638	+	0.765856i	0.0106957	+	0.0416571i
$339$	6.64259	−	10.4671i	0.360776	−	0.568492i
$340$	8.50973	−	5.73526i	0.461505	−	0.311038i
$341$	0.0708880	−	1.12673i	0.00383880	−	0.0610160i
$342$	1.01513	+	1.84652i	0.0548920	+	0.0998481i
$343$	4.42787	−	1.43870i	0.239082	−	0.0776825i
$344$	−4.44998	−	0.562163i	−0.239927	−	0.0303098i
$345$	−2.01496	+	12.4114i	−0.108482	+	0.668207i
$346$	−0.323972	+	0.304230i	−0.0174168	+	0.0163555i
$347$	−7.49514	−	7.98151i	−0.402360	−	0.428470i	0.495597	−	0.868552i	$-0.334949\pi$
$347$	−7.49514	−	7.98151i	−0.402360	−	0.428470i	−0.897957	+	0.440082i	$0.854949\pi$
$348$	0.891232	−	3.47112i	0.0477751	−	0.186072i
$349$	−22.7317	−	16.5155i	−1.21680	−	0.884057i	−0.220969	−	0.975281i	$-0.570922\pi$
$349$	−22.7317	−	16.5155i	−1.21680	−	0.884057i	−0.995830	+	0.0912242i	$0.970922\pi$
$350$	−18.5821	+	5.87931i	−0.993254	+	0.314262i
$351$	2.82685	−	2.05383i	0.150886	−	0.109625i
$352$	0.246281	+	0.622034i	0.0131268	+	0.0331545i
$353$	−0.106403	−	0.842267i	−0.00566326	−	0.0448293i	0.989030	−	0.147716i	$-0.0471921\pi$
$353$	−0.106403	−	0.842267i	−0.00566326	−	0.0448293i	−0.994693	+	0.102887i	$0.967192\pi$
$354$	−0.528115	−	0.290334i	−0.0280690	−	0.0154311i
$355$	−16.8067	+	7.19595i	−0.892009	+	0.381921i
$356$	−6.95207	+	14.7739i	−0.368459	+	0.783015i
$357$	−10.5150	+	14.4726i	−0.556511	+	0.765971i
$358$	0.603195	−	4.77478i	0.0318799	−	0.252355i
$359$	−29.0838	+	7.46746i	−1.53499	+	0.394117i	−0.919198	−	0.393795i	$-0.871162\pi$
$359$	−29.0838	+	7.46746i	−1.53499	+	0.394117i	−0.615788	+	0.787912i	$0.711162\pi$
$360$	2.22694	−	0.201829i	0.117370	−	0.0106373i
$361$	9.28082	+	11.2186i	0.488464	+	0.590452i
$362$	17.6362	+	14.5899i	0.926936	+	0.766828i
$363$	−8.90970	+	5.65427i	−0.467638	+	0.296772i
$364$	0.855227	+	13.5934i	0.0448260	+	0.712490i
$365$	0.458946	+	16.6534i	0.0240224	+	0.871677i
$366$	−7.08747	+	8.56728i	−0.370468	+	0.447819i
$367$	20.5648	−	3.92294i	1.07347	−	0.204776i	0.379801	−	0.925068i	$-0.375992\pi$
$367$	20.5648	−	3.92294i	1.07347	−	0.204776i	0.693671	+	0.720292i	$0.255992\pi$
$368$	3.30524	+	4.54928i	0.172298	+	0.237147i
$369$	7.78370	−	4.27912i	0.405203	−	0.222762i
$370$	6.63670	−	8.48805i	0.345026	−	0.441273i
$371$	42.0021	−	5.30610i	2.18064	−	0.275479i
$372$	−1.52689	+	0.718501i	−0.0791657	+	0.0372526i
$373$	−23.5340	+	1.48063i	−1.21855	+	0.0766644i	−0.659005	−	0.752139i	$-0.729022\pi$
$373$	−23.5340	+	1.48063i	−1.21855	+	0.0766644i	−0.559540	+	0.828803i	$0.689022\pi$
$374$	−3.07031			−0.158762
$375$	−8.91304	+	6.74964i	−0.460268	+	0.348550i
$376$	12.2378			0.631119
$377$	12.4974	−	0.786271i	0.643650	−	0.0404950i
$378$	−3.52701	+	1.65969i	−0.181410	+	0.0853651i
$379$	−27.0779	+	3.42073i	−1.39090	+	0.175711i	−0.784834	−	0.619705i	$-0.787252\pi$
$379$	−27.0779	+	3.42073i	−1.39090	+	0.175711i	−0.606063	+	0.795417i	$0.707252\pi$
$380$	−4.52970	+	1.29704i	−0.232369	+	0.0665368i
$381$	4.17137	−	2.29323i	0.213706	−	0.117486i
$382$	12.2140	+	16.8111i	0.624922	+	0.860131i
$383$	−35.5443	+	6.78044i	−1.81623	+	0.346464i	−0.979546	−	0.201223i	$-0.935509\pi$
$383$	−35.5443	+	6.78044i	−1.81623	+	0.346464i	−0.836683	+	0.547687i	$0.815509\pi$
$384$	0.637424	−	0.770513i	0.0325284	−	0.0393201i
$385$	5.59339	+	1.64849i	0.285066	+	0.0840151i
$386$	−1.51380	−	24.0611i	−0.0770503	−	1.22468i
$387$	3.78711	−	2.40337i	0.192509	−	0.122170i
$388$	−0.00226823	−	0.00187644i	−0.000115152	−	9.52618e-5i
$389$	9.92005	+	11.9913i	0.502967	+	0.607982i	0.959495	−	0.281727i	$-0.0909072\pi$
$389$	9.92005	+	11.9913i	0.502967	+	0.607982i	−0.456528	+	0.889709i	$0.650907\pi$
$390$	3.07528	+	7.18256i	0.155723	+	0.363703i
$391$	−24.9959	+	6.41786i	−1.26410	+	0.324565i
$392$	1.02703	−	8.12978i	0.0518728	−	0.410616i
$393$	0.124482	−	0.171334i	0.00627927	−	0.00864267i
$394$	1.56317	−	3.32191i	0.0787515	−	0.167355i
$395$	14.1902	−	23.7841i	0.713987	−	1.19671i
$396$	−0.586262	−	0.322300i	−0.0294608	−	0.0161962i
$397$	3.35558	+	26.5622i	0.168412	+	1.33312i	0.819047	+	0.573727i	$0.194503\pi$
$397$	3.35558	+	26.5622i	0.168412	+	1.33312i	−0.650635	+	0.759391i	$0.725497\pi$
$398$	3.51420	+	8.87585i	0.176151	+	0.444906i
$399$	6.64502	−	4.82789i	0.332667	−	0.241697i
$400$	−0.664984	+	4.95558i	−0.0332492	+	0.247779i
$401$	−19.3506	−	14.0590i	−0.966324	−	0.702075i	−0.0117128	−	0.999931i	$-0.503728\pi$
$401$	−19.3506	−	14.0590i	−0.966324	−	0.702075i	−0.954611	+	0.297856i	$0.903728\pi$
$402$	1.51713	−	5.90884i	0.0756677	−	0.294706i
$403$	−4.03638	−	4.29831i	−0.201066	−	0.214114i
$404$	−5.98660	+	5.62179i	−0.297845	+	0.279695i
$405$	−1.58724	+	1.57502i	−0.0788704	+	0.0782632i
$406$	−13.8591	−	1.75082i	−0.687817	−	0.0868916i
$407$	−3.06591	+	0.996175i	−0.151972	+	0.0493786i
$408$	2.21092	+	4.02164i	0.109457	+	0.199101i
$409$	−2.15001	+	34.1734i	−0.106311	+	1.68977i	0.478096	+	0.878308i	$0.341327\pi$
$409$	−2.15001	+	34.1734i	−0.106311	+	1.68977i	−0.584407	+	0.811461i	$0.698673\pi$
$410$	5.46748	+	19.0943i	0.270019	+	0.942999i
$411$	−6.24035	+	9.83321i	−0.307814	+	0.485037i
$412$	1.51467	+	5.89926i	0.0746226	+	0.290636i
$413$	−0.864787	+	2.18420i	−0.0425534	+	0.107478i
$414$	−5.44655	−	1.39844i	−0.267683	−	0.0687294i
$415$	−0.995366	−	6.44559i	−0.0488606	−	0.316402i
$416$	3.24881	+	1.28629i	0.159286	+	0.0630657i
$417$	−8.15386	−	3.83692i	−0.399296	−	0.187895i
$418$	1.34072	+	0.435627i	0.0655768	+	0.0213072i
$419$	−6.56055	−	34.3916i	−0.320504	−	1.68014i	−0.669340	−	0.742956i	$-0.733423\pi$
$419$	−6.56055	−	34.3916i	−0.320504	−	1.68014i	0.348837	−	0.937184i	$-0.386577\pi$
$420$	−1.86849	−	8.51356i	−0.0911732	−	0.415419i
$421$	7.89122	+	16.7697i	0.384595	+	0.817305i	0.999586	+	0.0287712i	$0.00915942\pi$
$421$	7.89122	+	16.7697i	0.384595	+	0.817305i	−0.614992	+	0.788534i	$0.710841\pi$
$422$	−23.6315	−	4.50795i	−1.15036	−	0.219444i
$423$	−9.42942	+	7.80070i	−0.458474	+	0.379283i
$424$	3.35621	−	10.3294i	0.162992	−	0.501638i
$425$	−20.0222	−	11.2096i	−0.971218	−	0.543748i
$426$	−2.52657	−	7.77599i	−0.122413	−	0.376748i
$427$	36.5945	+	23.2236i	1.77093	+	1.12387i
$428$	5.80140	−	10.5527i	0.280421	−	0.510084i
$429$	0.438033	−	2.29625i	0.0211485	−	0.110864i
$430$	3.36090	+	9.44966i	0.162077	+	0.455703i
$431$	7.17779	+	6.74039i	0.345742	+	0.324673i	0.837891	−	0.545838i	$-0.183788\pi$
$431$	7.17779	+	6.74039i	0.345742	+	0.324673i	−0.492149	+	0.870511i	$0.663788\pi$
$432$			1.00000i			0.0481125i
$433$	17.4047	−	18.5341i	0.836415	−	0.890692i	−0.158908	−	0.987293i	$-0.550797\pi$
$433$	17.4047	−	18.5341i	0.836415	−	0.890692i	0.995323	+	0.0966017i	$0.0307973\pi$
$434$	3.52459	+	5.55387i	0.169186	+	0.266594i
$435$	−7.82712	+	1.71784i	−0.375282	+	0.0823641i
$436$	−7.76331	+	3.07371i	−0.371795	+	0.147204i
$437$	11.8256	+	0.744004i	0.565696	+	0.0355906i
$438$	−7.43574	−	0.467817i	−0.355293	−	0.0223532i
$439$	24.8694	−	9.84651i	1.18695	−	0.469948i	0.310099	−	0.950704i	$-0.399638\pi$
$439$	24.8694	−	9.84651i	1.18695	−	0.469948i	0.876854	+	0.480756i	$0.159638\pi$
$440$	0.993626	−	1.11831i	0.0473693	−	0.0533132i
$441$	4.39077	+	6.91875i	0.209084	+	0.329464i
$442$	−10.9773	+	11.6896i	−0.522137	+	0.556020i
$443$		−	28.7644i		−	1.36664i	−0.730119	−	0.683320i	$-0.760535\pi$
$443$		−	28.7644i		−	1.36664i	0.730119	−	0.683320i	$-0.239465\pi$
$444$	3.51258	+	3.29853i	0.166700	+	0.156542i
$445$	36.4964	−	1.00580i	1.73009	−	0.0476793i
$446$	0.119761	−	0.627809i	0.00567085	−	0.0297276i
$447$	−4.09223	+	7.44373i	−0.193556	+	0.352076i
$448$	−3.29119	−	2.08865i	−0.155494	−	0.0986795i
$449$	−9.16757	−	28.2149i	−0.432644	−	1.33154i	−0.895481	−	0.445099i	$-0.853169\pi$
$449$	−9.16757	−	28.2149i	−0.432644	−	1.33154i	0.462837	−	0.886443i	$-0.346831\pi$
$450$	−2.64643	−	4.24222i	−0.124754	−	0.199980i
$451$	1.83632	−	5.65161i	0.0864688	−	0.266124i
$452$	−9.55198	+	7.90208i	−0.449287	+	0.371683i
$453$	17.5586	+	3.34948i	0.824974	+	0.157372i
$454$	4.89287	+	10.3979i	0.229634	+	0.487997i
$455$	26.2744	−	15.4019i	1.23176	−	0.722053i
$456$	−0.394842	−	2.06983i	−0.0184902	−	0.0969288i
$457$	4.08429	+	1.32707i	0.191055	+	0.0620776i	0.402982	−	0.915208i	$-0.367974\pi$
$457$	4.08429	+	1.32707i	0.191055	+	0.0620776i	−0.211927	+	0.977286i	$0.567974\pi$
$458$	6.25894	+	2.94523i	0.292461	+	0.137622i
$459$	−4.26703	−	1.68944i	−0.199168	−	0.0788562i
$460$	5.75168	−	11.1813i	0.268173	−	0.521330i
$461$	−27.6428	−	7.09747i	−1.28746	−	0.330562i	−0.457908	−	0.888999i	$-0.651401\pi$
$461$	−27.6428	−	7.09747i	−1.28746	−	0.330562i	−0.829547	+	0.558437i	$0.811401\pi$
$462$	−0.960002	+	2.42469i	−0.0446633	+	0.112807i
$463$	1.77650	+	6.91901i	0.0825610	+	0.321554i	0.996427	−	0.0844629i	$-0.0269175\pi$
$463$	1.77650	+	6.91901i	0.0825610	+	0.321554i	−0.913866	+	0.406017i	$0.866917\pi$
$464$	−1.92025	+	3.02583i	−0.0891452	+	0.140470i
$465$	2.97258	+	2.32422i	0.137850	+	0.107783i
$466$	1.57895	−	25.0966i	0.0731433	−	1.16258i
$467$	−16.3615	−	29.7614i	−0.757119	−	1.37719i	−0.920544	−	0.390638i	$-0.872254\pi$
$467$	−16.3615	−	29.7614i	−0.757119	−	1.37719i	0.163426	−	0.986556i	$-0.447746\pi$
$468$	−3.32316	+	1.07976i	−0.153613	+	0.0499120i
$469$	−23.5922	−	2.98039i	−1.08939	−	0.137622i
$470$	−12.3290	−	24.4299i	−0.568694	−	1.12687i
$471$	−8.32041	+	7.81339i	−0.383384	+	0.360022i
$472$	0.412550	+	0.439321i	0.0189891	+	0.0202214i
$473$	0.746260	−	2.90649i	0.0343131	−	0.133641i
$474$	10.0204	+	7.28022i	0.460250	+	0.334391i
$475$	7.15267	+	7.73576i	0.328187	+	0.354941i
$476$	14.4726	−	10.5150i	0.663350	−	0.481952i
$477$	3.99818	+	10.0982i	0.183064	+	0.462367i
$478$	−1.67900	−	13.2907i	−0.0767957	−	0.607900i
$479$	−22.8309	−	12.5514i	−1.04317	−	0.573487i	−0.134461	−	0.990919i	$-0.542930\pi$
$479$	−22.8309	−	12.5514i	−1.04317	−	0.573487i	−0.908708	+	0.417432i	$0.862930\pi$
$480$	−2.18032	−	0.496212i	−0.0995173	−	0.0226489i
$481$	−7.16882	+	15.2345i	−0.326870	+	0.694634i
$482$	14.2330	−	19.5900i	0.648295	−	0.892302i
$483$	−2.74721	+	21.7464i	−0.125003	+	0.989497i
$484$	10.2209	−	2.62428i	0.464586	−	0.119285i
$485$	−0.00146074	+	0.00641838i	−6.63288e−5	+	0.000291444i
$486$	−0.637424	−	0.770513i	−0.0289141	−	0.0349512i
$487$	22.8841	+	18.9313i	1.03698	+	0.857861i	0.990005	−	0.141035i	$-0.0450430\pi$
$487$	22.8841	+	18.9313i	1.03698	+	0.857861i	0.0469714	+	0.998896i	$0.485043\pi$
$488$	9.38802	−	5.95782i	0.424976	−	0.269698i
$489$	0.430004	+	6.83472i	0.0194455	+	0.309077i
$490$	−17.2638	+	6.14010i	−0.779900	+	0.277382i
$491$	−15.9265	+	19.2518i	−0.718753	+	0.868823i	−0.995755	−	0.0920462i	$-0.970659\pi$
$491$	−15.9265	+	19.2518i	−0.718753	+	0.868823i	0.277002	+	0.960869i	$0.410659\pi$
$492$	−8.72506	+	1.66439i	−0.393356	+	0.0750367i
$493$	−9.66715	−	13.3057i	−0.435387	−	0.599258i
$494$	6.45206	−	3.54705i	0.290292	−	0.159589i
$495$	−0.0527667	+	1.49503i	−0.00237169	+	0.0671967i
$496$	1.67419	−	0.211499i	0.0751734	−	0.00949661i
$497$	−28.8374	+	13.5699i	−1.29354	+	0.608692i
$498$	2.91097	−	0.183143i	0.130444	−	0.00820682i
$499$	−11.7514			−0.526064			−0.263032	−	0.964787i	$-0.584723\pi$
$499$	−11.7514			−0.526064			−0.263032	+	0.964787i	$0.584723\pi$
$500$	10.5626	−	3.66501i	0.472372	−	0.163904i
$501$	11.4766			0.512739
$502$	−2.22179	+	0.139783i	−0.0991632	+	0.00623882i
$503$	13.3704	−	6.29162i	0.596156	−	0.280530i	−0.103934	−	0.994584i	$-0.533143\pi$
$503$	13.3704	−	6.29162i	0.596156	−	0.280530i	0.700090	+	0.714055i	$0.253143\pi$
$504$	3.86726	−	0.488549i	0.172262	−	0.0217617i
$505$	17.2537	+	6.28715i	0.767782	+	0.279774i
$506$	−3.29668	+	1.81236i	−0.146555	+	0.0805694i
$507$	0.464760	+	0.639688i	0.0206407	+	0.0284095i
$508$	−4.67586	+	0.891968i	−0.207458	+	0.0395747i
$509$	−7.83924	+	9.47601i	−0.347468	+	0.420017i	−0.915076	−	0.403283i	$-0.867869\pi$
$509$	−7.83924	+	9.47601i	−0.347468	+	0.420017i	0.567607	+	0.823299i	$0.307869\pi$
$510$	5.80085	−	8.46515i	0.256866	−	0.374843i
$511$	1.82355	+	28.9845i	0.0806691	+	1.28220i
$512$	−0.844328	+	0.535827i	−0.0373144	+	0.0236804i
$513$	1.62359	+	1.34315i	0.0716833	+	0.0593016i
$514$	12.2419	+	14.7979i	0.539966	+	0.652707i
$515$	10.2505	−	8.96687i	0.451691	−	0.395128i
$516$	−4.34443	+	1.11546i	−0.191253	+	0.0491054i
$517$	−1.02614	+	8.12274i	−0.0451296	+	0.357238i
$518$	11.0402	−	15.1956i	0.485080	−	0.667655i
$519$	−0.189227	+	0.402128i	−0.00830615	+	0.0176515i
$520$	−0.705227	−	7.78133i	−0.0309262	−	0.341234i
$521$	5.42859	+	2.98439i	0.237831	+	0.130749i	0.596213	−	0.802826i	$-0.296671\pi$
$521$	5.42859	+	2.98439i	0.237831	+	0.130749i	−0.358382	+	0.933575i	$0.616671\pi$
$522$	−0.449158	−	3.55545i	−0.0196591	−	0.155618i
$523$	−16.0603	−	40.5638i	−0.702270	−	1.77373i	−0.630338	−	0.776321i	$-0.717084\pi$
$523$	−16.0603	−	40.5638i	−0.702270	−	1.77373i	−0.0719320	−	0.997410i	$-0.522916\pi$
$524$	−0.171334	+	0.124482i	−0.00748477	+	0.00543800i
$525$	−15.1129	+	12.3070i	−0.659579	+	0.537120i
$526$	−20.9580	−	15.2269i	−0.913811	−	0.663923i
$527$	−1.92596	+	7.50114i	−0.0838963	+	0.326755i
$528$	0.457972	+	0.487691i	0.0199307	+	0.0212240i
$529$	−6.28411	+	5.90117i	−0.273222	+	0.256573i
$530$	−24.0013	+	3.70642i	−1.04255	+	0.160997i
$531$	−0.597908	−	0.0755334i	−0.0259470	−	0.00327787i
$532$	−7.81169	+	2.53817i	−0.338679	+	0.110044i
$533$	−14.9520	−	27.1977i	−0.647645	−	1.17806i
$534$	−1.02524	+	16.2957i	−0.0443663	+	0.705182i
$535$	−26.9105	−	0.949799i	−1.16344	−	0.0410634i
$536$	−3.26881	+	5.15082i	−0.141191	+	0.222482i
$537$	−1.19688	−	4.66153i	−0.0516491	−	0.201160i
$538$	−2.26926	+	5.73149i	−0.0978346	+	0.247102i
$539$	5.30993	+	1.36336i	0.228715	+	0.0587240i
$540$	1.99626	−	1.00745i	0.0859053	−	0.0433536i
$541$	−10.2642	−	4.06387i	−0.441290	−	0.174719i	0.136963	−	0.990576i	$-0.456266\pi$
$541$	−10.2642	−	4.06387i	−0.441290	−	0.174719i	−0.578254	+	0.815857i	$0.696266\pi$
$542$	13.3933	+	6.30239i	0.575290	+	0.270711i
$543$	21.7686	+	7.07304i	0.934179	+	0.303533i
$544$	−0.859950	−	4.50802i	−0.0368701	−	0.193280i
$545$	13.9571	+	12.4010i	0.597854	+	0.531199i
$546$	5.79925	+	12.3240i	0.248185	+	0.527420i
$547$	−8.65287	−	1.65062i	−0.369970	−	0.0705755i	−0.000956361	−	1.00000i	$-0.500304\pi$
$547$	−8.65287	−	1.65062i	−0.369970	−	0.0705755i	−0.369014	+	0.929424i	$0.620304\pi$
$548$	8.97355	−	7.42357i	0.383331	−	0.317119i
$549$	−3.43594	+	10.5747i	−0.146642	+	0.451318i
$550$	−3.23346	−	0.856900i	−0.137875	−	0.0365383i
$551$	2.33352	+	7.18184i	0.0994114	+	0.305957i
$552$	4.74784	+	3.01307i	0.202081	+	0.128245i
$553$	23.2591	−	42.3081i	0.989076	−	1.79912i
$554$	3.47326	−	18.2074i	0.147565	−	0.773560i
$555$	3.04599	−	10.3351i	0.129295	−	0.438702i
$556$	6.56911	+	6.16881i	0.278592	+	0.261616i
$557$		−	33.3288i		−	1.41219i	−0.708118	−	0.706094i	$-0.750456\pi$
$557$		−	33.3288i		−	1.41219i	0.708118	−	0.706094i	$-0.249544\pi$
$558$	−1.15517	+	1.23013i	−0.0489023	+	0.0520757i
$559$	−8.39781	−	13.2328i	−0.355190	−	0.559689i
$560$	−0.853791	+	8.67427i	−0.0360792	+	0.366555i
$561$	−2.85471	+	1.13026i	−0.120526	+	0.0477195i
$562$	28.1847	+	1.77323i	1.18890	+	0.0747992i
$563$	−11.2287	−	0.706453i	−0.473235	−	0.0297734i	−0.175617	−	0.984459i	$-0.556192\pi$
$563$	−11.2287	−	0.706453i	−0.473235	−	0.0297734i	−0.297618	+	0.954685i	$0.596192\pi$
$564$	11.3785	−	4.50505i	0.479120	−	0.189697i
$565$	25.3977	+	11.1073i	1.06849	+	0.467287i
$566$	0.553179	+	0.871670i	0.0232518	+	0.0366390i
$567$	−2.66836	+	2.84152i	−0.112061	+	0.119333i
$568$			8.17616i			0.343064i
$569$	−7.99911	−	7.51166i	−0.335340	−	0.314905i	0.498523	−	0.866876i	$-0.333876\pi$
$569$	−7.99911	−	7.51166i	−0.335340	−	0.314905i	−0.833863	+	0.551971i	$0.813876\pi$
$570$	−3.73414	+	2.87345i	−0.156406	+	0.120356i
$571$	−5.58651	+	29.2855i	−0.233788	+	1.22556i	0.650823	+	0.759230i	$0.274424\pi$
$571$	−5.58651	+	29.2855i	−0.233788	+	1.22556i	−0.884611	+	0.466330i	$0.845576\pi$
$572$	−1.12618	+	2.04851i	−0.0470878	+	0.0856523i
$573$	17.5449	+	11.1343i	0.732947	+	0.465142i
$574$	10.6993	+	32.9290i	0.446579	+	1.37443i
$575$	−28.1152	−	0.217286i	−1.17249	−	0.00906145i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	11.0794	−	9.16565i	0.461240	−	0.381571i	−0.377583	−	0.925976i	$-0.623245\pi$
$577$	11.0794	−	9.16565i	0.461240	−	0.381571i	0.838822	+	0.544405i	$0.183245\pi$
$578$	3.98980	+	0.761094i	0.165954	+	0.0316574i
$579$	−10.2650	−	21.8142i	−0.426598	−	0.906567i
$580$	7.97488	+	0.784951i	0.331139	+	0.0325933i
$581$	−2.13041	−	11.1680i	−0.0883843	−	0.463327i
$582$	−0.00279971		0.000909679i	−0.000116052		3.77074e-5i
$583$	6.57459	+	3.09376i	0.272291	+	0.128131i
$584$	6.92724	+	2.74269i	0.286651	+	0.113493i
$585$	5.50340	+	5.54609i	0.227537	+	0.229303i
$586$	−21.3484	−	5.48133i	−0.881894	−	0.226432i
$587$	−8.93197	+	22.5596i	−0.368662	+	0.931134i	0.620487	+	0.784217i	$0.286935\pi$
$587$	−8.93197	+	22.5596i	−0.368662	+	0.931134i	−0.989149	+	0.146917i	$0.953065\pi$
$588$	−2.03786	−	7.93695i	−0.0840400	−	0.327314i
$589$	1.90530	−	3.00228i	0.0785067	−	0.123707i
$590$	0.461376	−	1.26615i	0.0189945	−	0.0521265i
$591$	0.230524	−	3.66408i	0.00948250	−	0.150720i
$592$	−2.32136	−	4.22254i	−0.0954073	−	0.173545i
$593$	−5.82289	+	1.89197i	−0.239117	+	0.0776940i	−0.426124	−	0.904665i	$-0.640121\pi$
$593$	−5.82289	+	1.89197i	−0.239117	+	0.0776940i	0.187007	+	0.982359i	$0.440121\pi$
$594$	−0.663739	−	0.0838498i	−0.0272335	−	0.00344040i
$595$	−35.5710	−	18.2978i	−1.45827	−	0.750136i
$596$	6.19218	−	5.81484i	0.253642	−	0.238185i
$597$	6.53484	+	6.95889i	0.267453	+	0.284809i
$598$	−4.88639	+	19.0312i	−0.199819	+	0.778245i
$599$	31.6959	+	23.0284i	1.29506	+	0.940917i	0.999894	−	0.0145293i	$-0.00462499\pi$
$599$	31.6959	+	23.0284i	1.29506	+	0.940917i	0.295166	+	0.955446i	$0.404625\pi$
$600$	1.20599	+	4.85238i	0.0492341	+	0.198098i
$601$	3.25237	−	2.36299i	0.132667	−	0.0963882i	−0.519473	−	0.854487i	$-0.673872\pi$
$601$	3.25237	−	2.36299i	0.132667	−	0.0963882i	0.652140	+	0.758099i	$0.273872\pi$
$602$	6.43625	+	16.2561i	0.262322	+	0.662549i
$603$	−0.764595	−	6.05239i	−0.0311367	−	0.246472i
$604$	−15.6641	−	8.61144i	−0.637365	−	0.350394i
$605$	−15.5358	−	17.7597i	−0.631618	−	0.722036i
$606$	−3.49668	+	7.43083i	−0.142043	+	0.301857i
$607$	0.131478	−	0.180964i	0.00533654	−	0.00734512i	−0.806340	−	0.591452i	$-0.798555\pi$
$607$	0.131478	−	0.180964i	0.00533654	−	0.00734512i	0.811677	+	0.584107i	$0.198555\pi$
$608$	−0.264097	+	2.09054i	−0.0107105	+	0.0847826i
$609$	−13.5304	+	3.47402i	−0.548280	+	0.140774i
$610$	−21.3513	−	12.7387i	−0.864489	−	0.515776i
$611$	27.2570	+	32.9481i	1.10270	+	1.33294i
$612$	3.53612	+	2.92533i	0.142939	+	0.118250i
$613$	22.6303	−	14.3617i	0.914031	−	0.580062i	0.00646871	−	0.999979i	$-0.497941\pi$
$613$	22.6303	−	14.3617i	0.914031	−	0.580062i	0.907562	+	0.419917i	$0.137941\pi$
$614$	−0.740233	−	11.7657i	−0.0298734	−	0.474824i
$615$	12.1126	+	15.7407i	0.488427	+	0.634726i
$616$	1.66229	−	2.00936i	0.0669754	−	0.0809593i
$617$	29.0681	−	5.54503i	1.17024	−	0.223234i	0.434608	−	0.900620i	$-0.356887\pi$
$617$	29.0681	−	5.54503i	1.17024	−	0.223234i	0.735628	+	0.677385i	$0.236887\pi$
$618$	3.57997	+	4.92740i	0.144007	+	0.198209i
$619$	−2.85873	+	1.57160i	−0.114902	+	0.0631679i	−0.538168	−	0.842837i	$-0.680883\pi$
$619$	−2.85873	+	1.57160i	−0.114902	+	0.0631679i	0.423266	+	0.906005i	$0.360883\pi$
$620$	−2.10887	−	3.12904i	−0.0846941	−	0.125665i
$621$	−5.57887	+	0.704776i	−0.223873	+	0.0282817i
$622$	10.0252	−	4.71751i	0.401975	−	0.189155i
$623$	63.5204	−	3.99637i	2.54489	−	0.160111i
$624$	3.49418			0.139879
$625$	−17.9575	−	17.3933i	−0.718301	−	0.695732i
$626$	16.7200			0.668267
$627$	1.40694	−	0.0885169i	0.0561876	−	0.00353503i
$628$	10.3277	−	4.85983i	0.412118	−	0.193928i
$629$	21.9395	−	2.77160i	0.874785	−	0.110511i
$630$	−4.87133	−	7.22787i	−0.194079	−	0.287965i
$631$	0.407969	−	0.224283i	0.0162410	−	0.00892857i	−0.473612	−	0.880733i	$-0.657050\pi$
$631$	0.407969	−	0.224283i	0.0162410	−	0.00892857i	0.489853	+	0.871805i	$0.337050\pi$
$632$	−7.28022	−	10.0204i	−0.289591	−	0.398588i
$633$	−23.6315	+	4.50795i	−0.939268	+	0.179175i
$634$	1.59955	−	1.93352i	0.0635261	−	0.0767898i
$635$	6.49128	+	8.43562i	0.257599	+	0.334757i
$636$	−0.681964	−	10.8395i	−0.0270416	−	0.429814i
$637$	24.1754	−	15.3422i	0.957863	−	0.607879i
$638$	−1.84735	−	1.52826i	−0.0731371	−	0.0605043i
$639$	−5.21168	−	6.29984i	−0.206171	−	0.249218i
$640$	1.92026	+	1.14568i	0.0759051	+	0.0452870i
$641$	−40.8687	+	10.4933i	−1.61422	+	0.414460i	−0.944594	−	0.328242i	$-0.893544\pi$
$641$	−40.8687	+	10.4933i	−1.61422	+	0.414460i	−0.669622	+	0.742702i	$0.733544\pi$
$642$	1.50929	−	11.9473i	0.0595671	−	0.471522i
$643$	−4.42679	+	6.09295i	−0.174576	+	0.240283i	−0.887334	−	0.461127i	$-0.847445\pi$
$643$	−4.42679	+	6.09295i	−0.174576	+	0.240283i	0.712759	+	0.701409i	$0.247445\pi$
$644$	9.33278	−	19.8332i	0.367763	−	0.781536i
$645$	6.60354	+	7.54885i	0.260014	+	0.297236i
$646$	−8.47423	−	4.65874i	−0.333414	−	0.183296i
$647$	2.23788	+	17.7146i	0.0879800	+	0.696433i	0.972988	+	0.230857i	$0.0741529\pi$
$647$	2.23788	+	17.7146i	0.0879800	+	0.696433i	−0.885008	+	0.465576i	$0.845847\pi$
$648$	0.368125	+	0.929776i	0.0144613	+	0.0365251i
$649$	−0.326186	+	0.236988i	−0.0128039	+	0.00930261i
$650$	−14.8231	+	9.24710i	−0.581409	+	0.362701i
$651$	5.32160	+	3.86637i	0.208570	+	0.151535i
$652$	1.70309	−	6.63309i	0.0666980	−	0.259772i
$653$	−14.1532	−	15.0716i	−0.553857	−	0.589798i	0.389727	−	0.920930i	$-0.372569\pi$
$653$	−14.1532	−	15.0716i	−0.553857	−	0.589798i	−0.943584	+	0.331132i	$0.892569\pi$
$654$	−6.08663	+	5.71573i	−0.238006	+	0.223503i
$655$	0.421108	+	0.216619i	0.0164540	+	0.00846400i
$656$	8.81235	+	1.11326i	0.344065	+	0.0434655i
$657$	−7.08579	+	2.30231i	−0.276443	+	0.0898218i
$658$	−22.9811	−	41.8026i	−0.895898	−	1.62963i
$659$	1.84139	−	29.2681i	0.0717304	−	1.14012i	−0.783334	−	0.621601i	$-0.786483\pi$
$659$	1.84139	−	29.2681i	0.0717304	−	1.14012i	0.855064	−	0.518522i	$-0.173517\pi$
$660$	0.512174	−	1.40555i	0.0199363	−	0.0547111i
$661$	8.71861	−	13.7383i	0.339115	−	0.534359i	−0.631383	−	0.775472i	$-0.717512\pi$
$661$	8.71861	−	13.7383i	0.339115	−	0.534359i	0.970497	+	0.241112i	$0.0775122\pi$
$662$	3.78392	+	14.7374i	0.147066	+	0.572785i
$663$	−5.90320	+	14.9098i	−0.229261	+	0.579048i
$664$	−2.82509	−	0.725360i	−0.109635	−	0.0281494i
$665$	12.9367	+	13.0371i	0.501664	+	0.505556i
$666$	4.48019	+	1.77383i	0.173604	+	0.0687346i
$667$	−18.2340	−	8.58029i	−0.706025	−	0.332230i
$668$	−10.9149	−	3.54648i	−0.422312	−	0.137217i
$669$	−0.119761	−	0.627809i	−0.00463023	−	0.0242725i
$670$	13.5755	+	1.33621i	0.524468	+	0.0516223i
$671$	3.16726	+	6.73076i	0.122271	+	0.259838i
$672$	−3.82895	−	0.730412i	−0.147705	−	0.0281763i
$673$	18.9012	−	15.6364i	0.728588	−	0.602741i	−0.197387	−	0.980326i	$-0.563245\pi$
$673$	18.9012	−	15.6364i	0.728588	−	0.602741i	0.925975	+	0.377585i	$0.123245\pi$
$674$	1.67968	−	5.16954i	0.0646990	−	0.199123i
$675$	−4.02225	−	2.97010i	−0.154817	−	0.114319i
$676$	−0.244339	−	0.751998i	−0.00939765	−	0.0289230i
$677$	13.5039	+	8.56985i	0.518998	+	0.329366i	0.769391	−	0.638778i	$-0.220560\pi$
$677$	13.5039	+	8.56985i	0.518998	+	0.329366i	−0.250393	+	0.968144i	$0.580560\pi$
$678$	−5.97225	+	10.8635i	−0.229363	+	0.417210i
$679$	−0.00215018	+	0.0112716i	−8.25162e−5	+	0.000432565i
$680$	−8.13282	+	6.25827i	−0.311879	+	0.239994i
$681$	8.37699	+	7.86652i	0.321007	+	0.301446i
$682$			1.12896i			0.0432301i
$683$	−17.9229	+	19.0860i	−0.685801	+	0.730304i	−0.973820	−	0.227321i	$-0.927003\pi$
$683$	−17.9229	+	19.0860i	−0.685801	+	0.730304i	0.288019	+	0.957625i	$0.407003\pi$
$684$	−1.12907	−	1.77913i	−0.0431711	−	0.0680268i
$685$	−23.8597	−	10.4347i	−0.911634	−	0.398689i
$686$	−4.32879	+	1.71389i	−0.165274	+	0.0654366i
$687$	6.90363	+	0.434340i	0.263390	+	0.0165711i
$688$	4.47650	+	0.281637i	0.170665	+	0.0107373i
$689$	35.2851	−	13.9704i	1.34425	−	0.532228i
$690$	1.23167	−	12.5134i	0.0468889	−	0.476378i
$691$	−10.5489	−	16.6225i	−0.401300	−	0.632348i	0.582244	−	0.813014i	$-0.302175\pi$
$691$	−10.5489	−	16.6225i	−0.401300	−	0.632348i	−0.983545	+	0.180666i	$0.942175\pi$
$692$	0.304230	−	0.323972i	0.0115651	−	0.0123156i
$693$			2.60782i			0.0990628i
$694$	7.98151	+	7.49514i	0.302974	+	0.284512i
$695$	5.69650	−	19.3284i	0.216081	−	0.733168i
$696$	−0.671520	+	3.52023i	−0.0254539	+	0.133434i
$697$	−19.6382	+	35.7218i	−0.743851	+	1.35306i
$698$	23.7239	+	15.0556i	0.897961	+	0.569863i
$699$	−7.77062	−	23.9155i	−0.293912	−	0.904568i
$700$	18.1762	−	7.03449i	0.686997	−	0.265879i
$701$	1.09173	−	3.35999i	0.0412340	−	0.126905i	−0.928320	−	0.371781i	$-0.878747\pi$
$701$	1.09173	−	3.35999i	0.0412340	−	0.126905i	0.969554	+	0.244876i	$0.0787472\pi$
$702$	−2.69231	+	2.22727i	−0.101615	+	0.0840631i
$703$	−9.97362	−	1.90257i	−0.376162	−	0.0717568i
$704$	−0.284853	−	0.605342i	−0.0107358	−	0.0228147i
$705$	−20.4565	−	18.1758i	−0.770435	−	0.684538i
$706$	0.159079	+	0.833924i	0.00598703	+	0.0313851i
$707$	30.4453	+	9.89226i	1.14501	+	0.372037i
$708$	0.545304	+	0.256600i	0.0204938	+	0.00964363i
$709$	39.6660	+	15.7049i	1.48969	+	0.589810i	0.965178	−	0.261594i	$-0.0842480\pi$
$709$	39.6660	+	15.7049i	1.48969	+	0.589810i	0.524511	+	0.851403i	$0.324248\pi$
$710$	16.3217	−	8.23705i	0.612544	−	0.309131i
$711$	11.9967	+	3.08023i	0.449912	+	0.115518i
$712$	6.01069	−	15.1813i	0.225260	−	0.568942i
$713$	2.35986	+	9.19104i	0.0883774	+	0.344207i
$714$	9.58547	−	15.1043i	0.358727	−	0.565263i
$715$	5.22391	+	0.184376i	0.195363	+	0.00689528i
$716$	−0.302194	+	4.80324i	−0.0112935	+	0.179505i
$717$	−6.45371	−	11.7393i	−0.241018	−	0.438411i
$718$	28.5576	−	9.27891i	1.06576	−	0.346286i
$719$	28.7372	+	3.63035i	1.07172	+	0.135389i	0.641337	−	0.767259i	$-0.278380\pi$
$719$	28.7372	+	3.63035i	1.07172	+	0.135389i	0.430379	+	0.902648i	$0.358380\pi$
$720$	−2.20987	+	0.341261i	−0.0823571	+	0.0127181i
$721$	17.3066	−	16.2520i	0.644530	−	0.605254i
$722$	−9.96693	−	10.6137i	−0.370931	−	0.395001i
$723$	6.02193	−	23.4539i	0.223958	−	0.872259i
$724$	−18.5175	−	13.4537i	−0.688196	−	0.500004i
$725$	−6.46731	−	16.7107i	−0.240190	−	0.620621i
$726$	8.53709	−	6.20256i	0.316841	−	0.230198i
$727$	7.95340	+	20.0880i	0.294975	+	0.745023i	0.999379	+	0.0352236i	$0.0112143\pi$
$727$	7.95340	+	20.0880i	0.294975	+	0.745023i	−0.704404	+	0.709799i	$0.748786\pi$
$728$	−1.70708	−	13.5129i	−0.0632685	−	0.500822i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	−1.50371	−	16.5917i	−0.0556550	−	0.614086i
$731$	−8.76452	+	18.6255i	−0.324167	+	0.688891i
$732$	6.53554	−	8.99540i	0.241561	−	0.332480i
$733$	6.41939	−	50.8147i	0.237106	−	1.87688i	−0.203346	−	0.979107i	$-0.565181\pi$
$733$	6.41939	−	50.8147i	0.237106	−	1.87688i	0.440451	−	0.897777i	$-0.354819\pi$
$734$	−20.2779	+	5.20647i	−0.748469	+	0.192174i
$735$	−13.7912	+	12.0642i	−0.508695	+	0.444993i
$736$	−3.58437	−	4.33276i	−0.132122	−	0.159708i
$737$	−3.14471	−	2.60153i	−0.115837	−	0.0958287i
$738$	−7.49965	+	4.75942i	−0.276066	+	0.175197i
$739$	0.483210	+	7.68041i	0.0177752	+	0.282528i	0.996866	+	0.0791059i	$0.0252065\pi$
$739$	0.483210	+	7.68041i	0.0177752	+	0.282528i	−0.979091	+	0.203423i	$0.934793\pi$
$740$	−6.09063	+	8.88802i	−0.223896	+	0.326730i
$741$	4.69322	−	5.67312i	0.172410	−	0.208407i
$742$	−41.5860	+	7.93296i	−1.52667	+	0.291228i
$743$	9.82152	+	13.5182i	0.360317	+	0.495933i	0.950237	−	0.311528i	$-0.100841\pi$
$743$	9.82152	+	13.5182i	0.360317	+	0.495933i	−0.589920	+	0.807462i	$0.700841\pi$
$744$	1.47877	−	0.812958i	0.0542142	−	0.0298045i
$745$	−17.8462	−	6.50304i	−0.653835	−	0.238253i
$746$	23.3946	−	2.95543i	0.856537	−	0.108206i
$747$	2.63913	−	1.24188i	0.0965608	−	0.0454380i
$748$	3.06425	−	0.192787i	0.112040	−	0.00704898i
$749$	−46.9407			−1.71517
$750$	8.47164	−	7.29598i	0.309341	−	0.266411i
$751$	27.0049			0.985423			0.492712	−	0.870193i	$-0.336006\pi$
$751$	27.0049			0.985423			0.492712	+	0.870193i	$0.336006\pi$
$752$	−12.2137	+	0.768421i	−0.445388	+	0.0280214i
$753$	−2.01431	+	0.947861i	−0.0734055	+	0.0345420i
$754$	−12.4234	+	1.56944i	−0.452433	+	0.0571556i
$755$	−1.40986	+	39.9453i	−0.0513099	+	1.45376i
$756$	3.41584	−	1.87788i	0.124233	−	0.0682977i
$757$	−20.0659	−	27.6183i	−0.729308	−	1.00381i	−0.999163	−	0.0409049i	$-0.986976\pi$
$757$	−20.0659	−	27.6183i	−0.729308	−	1.00381i	0.269855	−	0.962901i	$-0.413024\pi$
$758$	26.8097	−	5.11422i	0.973771	−	0.185757i
$759$	−2.39800	+	2.89868i	−0.0870418	+	0.105215i
$760$	4.43932	−	1.57890i	0.161031	−	0.0572729i
$761$	−1.64409	−	26.1321i	−0.0595983	−	0.947288i	−0.908274	−	0.418375i	$-0.862600\pi$
$761$	−1.64409	−	26.1321i	−0.0595983	−	0.947288i	0.848676	−	0.528913i	$-0.177400\pi$
$762$	−4.01915	+	2.55063i	−0.145598	+	0.0923996i
$763$	25.0778	+	20.7462i	0.907879	+	0.751063i
$764$	−13.2455	−	16.0110i	−0.479204	−	0.579258i
$765$	2.27727	−	10.0061i	0.0823348	−	0.361773i
$766$	35.0484	−	8.99890i	1.26635	−	0.325144i
$767$	−0.263927	+	2.08920i	−0.00952986	+	0.0754366i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−2.18106	+	4.63499i	−0.0786511	+	0.167142i	−0.940285	−	0.340388i	$-0.889441\pi$
$769$	−2.18106	+	4.63499i	−0.0786511	+	0.167142i	0.861634	+	0.507530i	$0.169441\pi$
$770$	−5.68586	−	1.29403i	−0.204904	−	0.0466336i
$771$	16.8297	+	9.25219i	0.606106	+	0.333209i
$772$	3.02162	+	23.9186i	0.108751	+	0.860849i
$773$	8.69551	+	21.9623i	0.312756	+	0.789931i	0.998094	+	0.0617063i	$0.0196542\pi$
$773$	8.69551	+	21.9623i	0.312756	+	0.789931i	−0.685339	+	0.728225i	$0.740346\pi$
$774$	−3.62872	+	2.63642i	−0.130432	+	0.0947642i
$775$	−4.12181	+	7.36219i	−0.148060	+	0.264458i
$776$	0.00238157	+	0.00173031i	8.54934e−5	+	6.21146e-5i
$777$	4.67108	−	18.1927i	0.167574	−	0.652658i
$778$	−10.6534	−	11.3447i	−0.381944	−	0.406729i
$779$	13.6438	−	12.8124i	0.488840	−	0.459051i
$780$	−3.52020	−	6.97529i	−0.126044	−	0.249755i
$781$	−5.42684	−	0.685569i	−0.194188	−	0.0245316i
$782$	24.5436	−	7.97470i	0.877677	−	0.285175i
$783$	−1.72646	−	3.14043i	−0.0616988	−	0.112230i
$784$	−0.514530	+	8.17822i	−0.0183761	+	0.292079i
$785$	−20.1060	−	15.7207i	−0.717615	−	0.561094i
$786$	−0.113478	+	0.178812i	−0.00404762	+	0.00637803i
$787$	−2.44286	−	9.51433i	−0.0870787	−	0.339149i	0.910084	−	0.414423i	$-0.136017\pi$
$787$	−2.44286	−	9.51433i	−0.0870787	−	0.339149i	−0.997163	+	0.0752743i	$0.976017\pi$
$788$	−1.35150	+	3.41351i	−0.0481453	+	0.121601i
$789$	−25.0916	−	6.44243i	−0.893285	−	0.229357i
$790$	−12.6688	+	24.6282i	−0.450735	+	0.876231i
$791$	44.9297	+	17.7889i	1.59752	+	0.632501i
$792$	0.605342	+	0.284853i	0.0215099	+	0.0101218i
$793$	36.9500	+	12.0058i	1.31213	+	0.426338i
$794$	−5.01681	−	26.2991i	−0.178040	−	0.933319i
$795$	−20.9514	+	12.2816i	−0.743070	+	0.435584i
$796$	−4.06458	−	8.63768i	−0.144065	−	0.306154i
$797$	6.12491	+	1.16839i	0.216955	+	0.0413864i	0.294713	−	0.955586i	$-0.404776\pi$
$797$	6.12491	+	1.16839i	0.216955	+	0.0413864i	−0.0777575	+	0.996972i	$0.524776\pi$
$798$	−6.32876	+	5.23560i	−0.224036	+	0.185338i
$799$	17.3554	−	53.4144i	0.613990	−	1.88967i
$800$	0.352508	−	4.98756i	0.0124630	−	0.176337i
$801$	5.04559	+	15.5287i	0.178277	+	0.548681i
$802$	20.1952	+	12.8163i	0.713117	+	0.452558i
$803$	−2.40128	+	4.36791i	−0.0847393	+	0.154140i
$804$	−1.14312	+	5.99244i	−0.0403147	+	0.211337i
$805$	−48.9944	+	1.35023i	−1.72683	+	0.0475892i
$806$	4.29831	+	4.03638i	0.151401	+	0.142175i
$807$			6.16437i			0.216996i
$808$	5.62179	−	5.98660i	0.197774	−	0.210608i
$809$	−5.23210	−	8.24447i	−0.183951	−	0.289860i	0.739821	−	0.672804i	$-0.234910\pi$
$809$	−5.23210	−	8.24447i	−0.183951	−	0.289860i	−0.923772	+	0.382944i	$0.874910\pi$
$810$	1.48521	−	1.67157i	0.0521849	−	0.0587331i
$811$	−37.0502	+	14.6692i	−1.30101	+	0.515106i	−0.913530	−	0.406772i	$-0.866654\pi$
$811$	−37.0502	+	14.6692i	−1.30101	+	0.515106i	−0.387480	+	0.921878i	$0.626654\pi$
$812$	13.9417	+	0.877139i	0.489259	+	0.0307815i
$813$	14.7728	+	0.929426i	0.518105	+	0.0325964i
$814$	2.99731	−	1.18672i	0.105056	−	0.0415945i
$815$	−14.9571	+	3.28268i	−0.523925	+	0.114987i
$816$	−2.45907	−	3.87488i	−0.0860848	−	0.135648i
$817$	6.46988	−	6.88972i	0.226353	−	0.241041i
$818$		−	34.2410i		−	1.19721i
$819$	9.92878	+	9.32375i	0.346940	+	0.325798i
$820$	−6.65563	−	18.7133i	−0.232425	−	0.653496i
$821$	−3.36323	+	17.6307i	−0.117377	+	0.615314i	0.874175	+	0.485610i	$0.161403\pi$
$821$	−3.36323	+	17.6307i	−0.117377	+	0.615314i	−0.991553	+	0.129704i	$0.958597\pi$
$822$	5.61060	−	10.2056i	0.195692	−	0.355963i
$823$	5.59040	+	3.54777i	0.194869	+	0.123668i	0.629682	−	0.776853i	$-0.283185\pi$
$823$	5.59040	+	3.54777i	0.194869	+	0.123668i	−0.434813	+	0.900521i	$0.643185\pi$
$824$	−1.88210	−	5.79251i	−0.0655661	−	0.201792i
$825$	−3.32184	+	0.393589i	−0.115652	+	0.0137030i
$826$	0.725933	−	2.23419i	0.0252585	−	0.0777375i
$827$	−4.34635	+	3.59561i	−0.151137	+	0.125032i	−0.709920	−	0.704283i	$-0.751269\pi$
$827$	−4.34635	+	3.59561i	−0.151137	+	0.125032i	0.558782	+	0.829314i	$0.311269\pi$
$828$	5.52361	+	1.05369i	0.191959	+	0.0366181i
$829$	−23.5124	−	49.9664i	−0.816619	−	1.73540i	−0.664835	−	0.746990i	$-0.731498\pi$
$829$	−23.5124	−	49.9664i	−0.816619	−	1.73540i	−0.151784	−	0.988414i	$-0.548502\pi$
$830$	1.39812	+	6.37037i	0.0485296	+	0.221119i
$831$	−3.47326	−	18.2074i	−0.120486	−	0.631609i
$832$	−3.32316	−	1.07976i	−0.115210	−	0.0374340i
$833$	−34.0274	−	16.0121i	−1.17898	−	0.554786i
$834$	8.37869	+	3.31736i	0.290130	+	0.114871i
$835$	3.91654	+	25.3619i	0.135537	+	0.877686i
$836$	−1.36543	−	0.350583i	−0.0472244	−	0.0121252i
$837$	−0.621209	+	1.56900i	−0.0214721	+	0.0542324i
$838$	8.70707	+	33.9118i	0.300781	+	1.17146i
$839$	5.13508	−	8.09159i	0.177283	−	0.279353i	−0.744053	−	0.668120i	$-0.767099\pi$
$839$	5.13508	−	8.09159i	0.177283	−	0.279353i	0.921336	+	0.388768i	$0.127099\pi$
$840$	2.39938	+	8.37944i	0.0827864	+	0.289118i
$841$	−1.01451	+	16.1252i	−0.0349831	+	0.556040i
$842$	−8.92863	−	16.2411i	−0.307701	−	0.559706i
$843$	26.8582	−	8.72677i	0.925046	−	0.300566i
$844$	23.8679	+	3.01522i	0.821568	+	0.103788i
$845$	−1.25502	+	1.24536i	−0.0431741	+	0.0428418i
$846$	8.92101	−	8.37738i	0.306711	−	0.288020i
$847$	−28.1577	−	29.9849i	−0.967510	−	1.03029i
$848$	−2.70100	+	10.5197i	−0.0927529	+	0.361249i
$849$	0.835215	+	0.606820i	0.0286645	+	0.0208260i
$850$	20.6865	+	9.93033i	0.709542	+	0.340607i
$851$	21.9210	−	15.9265i	0.751442	−	0.545954i
$852$	3.00985	+	7.60201i	0.103116	+	0.260440i
$853$	2.61930	+	20.7339i	0.0896833	+	0.709916i	0.971284	+	0.237921i	$0.0764660\pi$
$853$	2.61930	+	20.7339i	0.0896833	+	0.709916i	−0.881601	+	0.471995i	$0.843534\pi$
$854$	−37.9805	−	20.8800i	−1.29967	−	0.714498i
$855$	−2.41413	+	4.04630i	−0.0825614	+	0.138380i
$856$	−5.12734	+	10.8961i	−0.175249	+	0.372423i
$857$	−18.6864	+	25.7196i	−0.638314	+	0.878564i	−0.998524	−	0.0543071i	$-0.982705\pi$
$857$	−18.6864	+	25.7196i	−0.638314	+	0.878564i	0.360210	+	0.932871i	$0.382705\pi$
$858$	−0.292986	+	2.31922i	−0.0100024	+	0.0791770i
$859$	33.3047	−	8.55119i	1.13634	−	0.291763i	0.366762	−	0.930315i	$-0.380466\pi$
$859$	33.3047	−	8.55119i	1.13634	−	0.291763i	0.769579	+	0.638552i	$0.220466\pi$
$860$	−3.94762	−	9.21998i	−0.134613	−	0.314399i
$861$	22.0699	+	26.6779i	0.752140	+	0.909180i
$862$	−7.58686	−	6.27639i	−0.258409	−	0.213775i
$863$	−22.2481	+	14.1191i	−0.757334	+	0.480619i	−0.857584	−	0.514344i	$-0.828036\pi$
$863$	−22.2481	+	14.1191i	−0.757334	+	0.480619i	0.100250	+	0.994962i	$0.468036\pi$
$864$	−0.0627905	−	0.998027i	−0.00213618	−	0.0339536i
$865$	−0.953228	−	0.280937i	−0.0324107	−	0.00955215i
$866$	−16.2066	+	19.5904i	−0.550721	+	0.665708i
$867$	3.98980	−	0.761094i	0.135501	−	0.0258481i
$868$	−3.86637	−	5.32160i	−0.131233	−	0.180627i
$869$	7.26135	−	3.99196i	0.246324	−	0.135418i
$870$	7.70381	−	2.20592i	0.261184	−	0.0747877i
$871$	−21.1482	+	2.67163i	−0.716578	+	0.0905249i
$872$	7.55499	−	3.55511i	0.255844	−	0.120391i
$873$	−0.00293798		0.000184842i	−9.94354e−5		6.25595e-6i
$874$	−11.8490			−0.400798
$875$	−32.3543	−	29.1976i	−1.09377	−	0.987059i
$876$	7.45044			0.251727
$877$	11.1628	−	0.702303i	0.376940	−	0.0237151i	0.126809	−	0.991927i	$-0.459526\pi$
$877$	11.1628	−	0.702303i	0.376940	−	0.0237151i	0.250131	+	0.968212i	$0.419526\pi$
$878$	−24.2021	+	11.3886i	−0.816781	+	0.384348i
$879$	−21.8670	+	2.76245i	−0.737557	+	0.0931751i
$880$	−0.921446	+	1.17849i	−0.0310620	+	0.0397269i
$881$	2.09405	−	1.15122i	0.0705504	−	0.0387854i	−0.446088	−	0.894989i	$-0.647183\pi$
$881$	2.09405	−	1.15122i	0.0705504	−	0.0387854i	0.516638	+	0.856204i	$0.327183\pi$
$882$	−4.81654	−	6.62940i	−0.162181	−	0.223224i
$883$	−34.9381	+	6.66481i	−1.17576	+	0.224289i	−0.737999	−	0.674802i	$-0.764229\pi$
$883$	−34.9381	+	6.66481i	−1.17576	+	0.224289i	−0.437763	+	0.899090i	$0.644229\pi$
$884$	10.2216	−	12.3559i	0.343791	−	0.415572i
$885$	−0.0371238	−	1.34708i	−0.00124790	−	0.0452815i
$886$	1.80613	+	28.7077i	0.0606783	+	0.964453i
$887$	−28.2703	+	17.9409i	−0.949223	+	0.602396i	−0.917771	−	0.397110i	$-0.870013\pi$
$887$	−28.2703	+	17.9409i	−0.949223	+	0.602396i	−0.0314523	+	0.999505i	$0.510013\pi$
$888$	−3.71277	−	3.07147i	−0.124592	−	0.103072i
$889$	11.8275	+	14.2970i	0.396682	+	0.479506i
$890$	−36.3612	+	3.29544i	−1.21883	+	0.110463i
$891$	−0.647996	+	0.166377i	−0.0217087	+	0.00557384i
$892$	−0.0801043	+	0.634090i	−0.00268209	+	0.0212309i
$893$	−15.1573	+	20.8622i	−0.507218	+	0.698126i
$894$	3.61676	−	7.68600i	0.120962	−	0.257058i
$895$	9.89295	−	4.23575i	0.330685	−	0.141586i
$896$	3.41584	+	1.87788i	0.114115	+	0.0627354i
$897$	2.46261	+	19.4936i	0.0822243	+	0.650872i
$898$	10.9211	+	27.5836i	0.364442	+	0.920475i
$899$	−4.89253	+	3.55463i	−0.163175	+	0.118554i
$900$	2.90758	+	4.06768i	0.0969192	+	0.135589i
$901$	−40.3248	−	29.2977i	−1.34341	−	0.976047i
$902$	−1.47783	+	5.75576i	−0.0492063	+	0.191646i
$903$	11.9685	+	12.7452i	0.398288	+	0.424134i
$904$	9.03696	−	8.48627i	0.300565	−	0.282249i
$905$	−8.20175	+	50.5196i	−0.272635	+	1.67933i
$906$	−17.7342	−	2.24036i	−0.589181	−	0.0744308i
$907$	34.9326	−	11.3503i	1.15992	−	0.376880i	0.335047	−	0.942202i	$-0.391248\pi$
$907$	34.9326	−	11.3503i	1.15992	−	0.376880i	0.824871	+	0.565322i	$0.191248\pi$
$908$	−5.53610	−	10.0701i	−0.183722	−	0.334189i
$909$	−0.515663	+	8.19622i	−0.0171035	+	0.271852i
$910$	−25.2555	+	17.0213i	−0.837211	+	0.564251i
$911$	6.13472	−	9.66677i	0.203252	−	0.320275i	−0.727377	−	0.686238i	$-0.759261\pi$
$911$	6.13472	−	9.66677i	0.203252	−	0.320275i	0.930629	+	0.365964i	$0.119261\pi$
$912$	0.524028	+	2.04096i	0.0173523	+	0.0675828i
$913$	0.718333	−	1.81430i	0.0237733	−	0.0600446i
$914$	−4.15956	−	1.06799i	−0.137586	−	0.0353261i
$915$	−24.5414	−	3.98424i	−0.811313	−	0.131715i
$916$	−6.43152	−	2.54642i	−0.212504	−	0.0841361i
$917$	0.746954	+	0.351490i	0.0246666	+	0.0116072i
$918$	4.36469	+	1.41817i	0.144056	+	0.0468067i
$919$	7.74739	+	40.6132i	0.255563	+	1.33971i	0.846241	+	0.532800i	$0.178860\pi$
$919$	7.74739	+	40.6132i	0.255563	+	1.33971i	−0.590679	+	0.806907i	$0.701140\pi$
$920$	−5.03825	+	11.5204i	−0.166106	+	0.379815i
$921$	−5.01948	−	10.6669i	−0.165398	−	0.351488i
$922$	28.0339	+	5.34776i	0.923249	+	0.176119i
$923$	−22.0128	+	18.2106i	−0.724560	+	0.599408i
$924$	0.805860	−	2.48018i	0.0265108	−	0.0815920i
$925$	23.8788	+	3.20427i	0.785130	+	0.105356i
$926$	−2.20744	−	6.79381i	−0.0725411	−	0.223259i
$927$	5.14247	+	3.26351i	0.168901	+	0.107188i
$928$	1.72646	−	3.14043i	0.0566740	−	0.103090i
$929$	−10.1297	+	53.1019i	−0.332345	+	1.74222i	0.287765	+	0.957701i	$0.407088\pi$
$929$	−10.1297	+	53.1019i	−0.332345	+	1.74222i	−0.620110	+	0.784515i	$0.712912\pi$
$930$	−3.11265	−	2.13299i	−0.102068	−	0.0699434i
$931$	12.5870	+	11.8200i	0.412522	+	0.387384i
$932$			25.1463i			0.823693i
$933$	7.58458	−	8.07676i	0.248308	−	0.264421i
$934$	18.1979	+	28.6753i	0.595454	+	0.938286i
$935$	−3.47193	−	5.92282i	−0.113544	−	0.193697i
$936$	3.24881	−	1.28629i	0.106191	−	0.0420438i
$937$	15.3351	+	0.964802i	0.500975	+	0.0315187i	0.311268	−	0.950322i	$-0.399246\pi$
$937$	15.3351	+	0.964802i	0.500975	+	0.0315187i	0.189707	+	0.981841i	$0.439246\pi$
$938$	23.7328	+	1.49314i	0.774904	+	0.0487528i
$939$	15.5459	−	6.15506i	0.507321	−	0.200863i
$940$	13.8386	+	23.6076i	0.451366	+	0.769994i
$941$	13.2086	+	20.8134i	0.430588	+	0.678498i	0.988469	−	0.151423i	$-0.0483856\pi$
$941$	13.2086	+	20.8134i	0.430588	+	0.678498i	−0.557881	+	0.829921i	$0.688386\pi$
$942$	7.81339	−	8.32041i	0.254574	−	0.271094i
$943$			49.9476i			1.62652i
$944$	−0.439321	−	0.412550i	−0.0142987	−	0.0134273i
$945$	−7.19001	−	4.92704i	−0.233891	−	0.160277i
$946$	−0.562287	+	2.94761i	−0.0182815	+	0.0958351i
$947$	2.89923	−	5.27368i	0.0942123	−	0.171372i	−0.825001	−	0.565131i	$-0.808826\pi$
$947$	2.89923	−	5.27368i	0.0942123	−	0.171372i	0.919214	+	0.393759i	$0.128826\pi$
$948$	−10.4577	−	6.63667i	−0.339651	−	0.215549i
$949$	8.04470	+	24.7590i	0.261142	+	0.803712i
$950$	−7.62429	−	7.27138i	−0.247365	−	0.235915i
$951$	0.775444	−	2.38657i	0.0251455	−	0.0773899i
$952$	−13.7838	+	11.4029i	−0.446735	+	0.369572i
$953$	37.9770	+	7.24450i	1.23020	+	0.234672i	0.761194	−	0.648525i	$-0.224614\pi$
$953$	37.9770	+	7.24450i	1.23020	+	0.234672i	0.469002	+	0.883197i	$0.344614\pi$
$954$	−4.62436	−	9.82727i	−0.149719	−	0.318170i
$955$	−18.6180	+	42.5716i	−0.602465	+	1.37759i
$956$	2.51021	+	13.1590i	0.0811861	+	0.425593i
$957$	−2.28021	−	0.740885i	−0.0737087	−	0.0239494i
$958$	23.5739	+	11.0930i	0.761639	+	0.358400i
$959$	−42.2089	−	16.7117i	−1.36300	−	0.539649i
$960$	2.20717	+	0.358330i	0.0712361	+	0.0115650i
$961$	−27.2679	−	7.00121i	−0.879610	−	0.225845i
$962$	6.19809	−	15.6546i	0.199834	−	0.504724i
$963$	−2.99478	−	11.6639i	−0.0965056	−	0.375864i
$964$	−12.9748	+	20.4451i	−0.417892	+	0.658492i
$965$	44.7036	−	30.1287i	1.43906	−	0.969876i
$966$	1.37632	−	21.8760i	0.0442825	−	0.703850i
$967$	−2.73772	−	4.97990i	−0.0880392	−	0.160143i	0.828621	−	0.559810i	$-0.189126\pi$
$967$	−2.73772	−	4.97990i	−0.0880392	−	0.160143i	−0.916660	+	0.399667i	$0.869126\pi$
$968$	−10.0359	+	3.26088i	−0.322568	+	0.104809i
$969$	−9.59413	−	1.21202i	−0.308208	−	0.0389357i
$970$	0.00105484	−	0.00649743i	3.38690e−5	−	0.000208620i
$971$	24.6455	−	23.1436i	0.790911	−	0.742715i	−0.179608	−	0.983738i	$-0.557483\pi$
$971$	24.6455	−	23.1436i	0.790911	−	0.742715i	0.970519	+	0.241023i	$0.0774830\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	8.73570	−	34.0233i	0.280054	−	1.09074i
$974$	−24.0276	−	17.4571i	−0.769895	−	0.559361i
$975$	−10.3781	+	14.0545i	−0.332364	+	0.450103i
$976$	−8.99540	+	6.53554i	−0.287936	+	0.209198i
$977$	18.4209	+	46.5259i	0.589337	+	1.48850i	0.851965	+	0.523599i	$0.175411\pi$
$977$	18.4209	+	46.5259i	0.589337	+	1.48850i	−0.262628	+	0.964897i	$0.584589\pi$
$978$	−0.858312	−	6.79424i	−0.0274458	−	0.217256i
$979$	9.57241	+	5.26248i	0.305936	+	0.168190i
$980$	16.8442	−	7.21199i	0.538069	−	0.230379i
$981$	−3.55511	+	7.55499i	−0.113506	+	0.241212i
$982$	14.6862	−	20.2139i	0.468657	−	0.645051i
$983$	−7.68152	+	60.8055i	−0.245002	+	1.93939i	0.0872135	+	0.996190i	$0.472204\pi$
$983$	−7.68152	+	60.8055i	−0.245002	+	1.93939i	−0.332216	+	0.943203i	$0.607796\pi$
$984$	8.60334	−	2.20896i	0.274264	−	0.0704191i
$985$	8.17581	−	0.740979i	0.260503	−	0.0236095i
$986$	10.4835	+	12.6724i	0.333864	+	0.403572i
$987$	−36.7559	−	30.4071i	−1.16995	−	0.967869i
$988$	−6.21661	+	3.94518i	−0.197777	+	0.125513i
$989$	1.58371	+	25.1723i	0.0503590	+	0.800433i
$990$	−0.0412112	−	1.49539i	−0.00130978	−	0.0475267i
$991$	−23.1304	+	27.9598i	−0.734761	+	0.888174i	−0.997045	−	0.0768170i	$-0.975524\pi$
$991$	−23.1304	+	27.9598i	−0.734761	+	0.888174i	0.262284	+	0.964991i	$0.415524\pi$
$992$	−1.65761	+	0.316205i	−0.0526291	+	0.0100395i
$993$	8.94340	+	12.3095i	0.283810	+	0.390631i
$994$	27.9285	−	15.3538i	0.885838	−	0.486993i
$995$	−13.1482	+	16.8160i	−0.416826	+	0.533102i
$996$	−2.89373	+	0.365563i	−0.0916912	+	0.0115833i
$997$	−10.4727	+	4.92810i	−0.331675	+	0.156074i	−0.584404	−	0.811463i	$-0.698672\pi$
$997$	−10.4727	+	4.92810i	−0.331675	+	0.156074i	0.252729	+	0.967537i	$0.418672\pi$
$998$	11.7282	−	0.737876i	0.371250	−	0.0233570i
$999$	4.81856			0.152453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.469.2	yes	280
125.4	even	50	inner	750.2.o.b.379.2	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.379.2	✓	280	125.4	even	50	inner
750.2.o.b.469.2	yes	280	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.24970 - 1.85425i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.29119 - 3.15355i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-1.24970 - 1.85425i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.29119 - 3.15355i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(1.36366 + 1.77212i) q^{10} +(-0.0420078 - 0.667694i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(-2.69231 - 2.22727i) q^{13} +(2.48468 + 3.00346i) q^{14} +(1.92026 + 1.14568i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.575193 + 4.55312i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(0.897184 - 1.90661i) q^{19} +(-1.47225 - 1.68300i) q^{20} +(3.41584 + 1.87788i) q^{21} +(0.0838498 + 0.663739i) q^{22} +(2.07004 + 5.22833i) q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.87650 + 4.63452i) q^{25} +(2.82685 + 2.05383i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-2.66836 - 2.84152i) q^{28} +(-2.61241 + 2.45322i) q^{29} +(-1.98841 - 1.02284i) q^{30} +(1.67419 + 0.211499i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(0.322300 + 0.586262i) q^{33} +(0.288165 - 4.58025i) q^{34} +(-2.98417 + 8.18942i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.19833 - 4.66718i) q^{37} +(-0.775696 + 1.95918i) q^{38} +(3.38441 + 0.868968i) q^{39} +(1.57502 + 1.58724i) q^{40} +(8.25864 + 3.26983i) q^{41} +(-3.52701 - 1.65969i) q^{42} +(4.26582 + 1.38605i) q^{43} +(-0.125361 - 0.657164i) q^{44} +(-2.22531 - 0.219033i) q^{45} +(-2.39425 - 5.08804i) q^{46} +(-12.0211 - 2.29314i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-2.53221 + 7.79333i) q^{49} +(1.58179 - 4.74320i) q^{50} +(-1.41817 - 4.36469i) q^{51} +(-2.95023 - 1.87228i) q^{52} +(-5.23230 + 9.51751i) q^{53} +(0.187381 - 0.982287i) q^{54} +(-1.18558 + 0.912311i) q^{55} +(2.84152 + 2.66836i) q^{56} +2.10716i q^{57} +(2.45322 - 2.61241i) q^{58} +(-0.322922 - 0.508843i) q^{59} +(2.04871 + 0.895973i) q^{60} +(-10.3381 + 4.09315i) q^{61} +(-1.68417 - 0.105959i) q^{62} +(-3.89031 - 0.244757i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-0.765341 + 7.77565i) q^{65} +(-0.358476 - 0.564868i) q^{66} +(4.17608 - 4.44707i) q^{67} +4.58931i q^{68} +(-4.09915 - 3.84936i) q^{69} +(2.46406 - 8.36064i) q^{70} +(1.53206 - 8.03134i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-6.29061 - 3.99215i) q^{73} +(1.48902 + 4.58273i) q^{74} +(-0.275379 - 4.99241i) q^{75} +(0.651147 - 2.00402i) q^{76} +(-2.00936 + 1.66229i) q^{77} +(-3.43229 - 0.654744i) q^{78} +(5.27364 + 11.2070i) q^{79} +(-1.67157 - 1.48521i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-8.44766 - 2.74481i) q^{82} +(2.63913 + 1.24188i) q^{83} +(3.62427 + 1.43495i) q^{84} +(9.16145 - 4.62349i) q^{85} +(-4.34443 - 1.11546i) q^{86} +(1.31925 - 3.33205i) q^{87} +(0.166377 + 0.647996i) q^{88} +(-8.74891 + 13.7861i) q^{89} +(2.23468 + 0.0788722i) q^{90} +(-0.855227 + 13.5934i) q^{91} +(2.70900 + 4.92766i) q^{92} +(-1.60491 + 0.521465i) q^{93} +(12.1413 + 1.53381i) q^{94} +(-4.65655 + 0.719091i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-0.00201516 - 0.00214593i) q^{97} +(2.03786 - 7.93695i) q^{98} +(-0.541244 - 0.393237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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